# Primes - allocate descendants to their ancestors

Primes - allocate descendants to their ancestors
You are encouraged to solve this task according to the task description, using any language you may know.

The concept, is to add the decomposition into prime factors of a number to get its 'ancestors'.

The objective is to demonstrate that the choice of the algorithm can be crucial in term of performance. This solution could be compared to the solution that would use the decomposition into primes for all the numbers between 1 and 333.

The problem is to list, for a delimited set of ancestors (from 1 to 99) :

- the total of their own ancestors (LEVEL),

- their own ancestors (ANCESTORS),

- the total of the direct descendants (DESCENDANTS),

- all the direct descendants.

You only have to consider the prime factors < 100.

A grand total of the descendants has to be printed at the end of the list.

The task should be accomplished in a reasonable time-frame.

Example :

```46 = 2*23 --> 2+23 = 25, is the parent of 46.
25 = 5*5  --> 5+5  = 10, is the parent of 25.
10 = 2*5  --> 2+5  = 7,  is the parent of 10.
7 is a prime factor and, as such, has no parent.

46 has 3 ancestors (7, 10 and 25).
46 has 557 descendants.```

The list layout and the output for Parent [46] :

```[46] Level: 3
Ancestors: 7, 10, 25
Descendants: 557
129, 205, 246, 493, 518, 529, 740, 806, 888, 999, 1364, 1508, 1748, 2552, 2871, 3128, 3255, 3472, 3519, 3875, 3906, 4263, 4650, 4960, 5075, 5415, 5580, 5776, 5952, 6090, 6279, 6496, 6498, 6696, 6783, 7250, 7308, 7475, 7533, 8075, 8151, 8619, 8700, 8855, 8970, 9280, 9568, 9690, 10115, 10336, 10440, 10626, 10764, 11136, 11495, 11628, 11745, 12103, 12138, 12155, 12528, 12650, 13794, 14094, 14399, 14450, 14586, 15180, 15379, 15778, 16192, 17290, 17303, 17340, 18216, 18496, 20482, 20493, 20570, 20748, 20808, 21658, 21970, 22540, 23409, 24684, 24700, 26026, 26364, 27048, 29260, 29282, 29640, 30429, 30940, 31616, 32200, 33345, 35112, 35568, 36225, 36652, 37128, 37180, 38640, 39501, 40014, 41216, 41769, 41800, 43125, 43470, 44044, 44200, 44616, 46000, 46368, 47025, 49725, 50160, 50193, 51750, 52136, 52164, 52360, 53040, 53504, 55200, 56430, 56576, 58653, 58880, 58905, 59670, 60192, 62100, 62832, 62920, 63648, 66240, 66248, 67716, 69825, 70125, 70656, 70686, 70785, 71604, 74480, 74520, 74529, 74536, 74800, 75504, 79488, 83125, 83790, 83835, 83853, 84150, 84942, 87465, 88725, 89376, 89424, 89760, 93296, 94640, 95744, 99750, 99825, 100548, 100602, 100980, 104125, 104958, 105105, 105625, 106400, 106470, 106480, 107712, 112112, 113568, 118750, 119700, 119790, 121176, 124509, 124950, 125125, 126126, 126750, 127680, 127764, 127776, 133280, 135200, 136192, 136323, 142500, 143640, 143748, 148225, 148750, 149940, 150150, 152000, 152100, 153216, 156065, 159936, 160160, 161595, 162240, 171000, 172368, 173056, 177870, 178500, 178750, 179928, 180180, 182400, 182520, 184877, 187278, 189728, 190400, 192192, 192375, 193914, 194560, 194688, 202419, 205200, 205335, 211750, 212500, 213444, 214200, 214500, 216216, 218880, 219024, 222950, 228480, 228800, 230850, 233472, 240975, 243243, 243712, 246240, 246402, 254100, 255000, 257040, 257400, 262656, 264110, 267540, 271040, 272000, 274176, 274560, 277020, 285376, 286875, 289170, 289575, 292864, 295488, 302500, 304920, 306000, 308448, 308880, 316932, 318500, 321048, 325248, 326400, 329472, 332424, 343035, 344250, 347004, 347490, 348160, 361179, 363000, 365904, 367200, 370656, 373977, 377300, 382200, 387200, 391680, 407680, 408375, 411642, 413100, 416988, 417792, 429975, 435600, 440640, 452760, 455000, 458640, 464640, 470016, 470596, 482944, 489216, 490050, 495616, 495720, 509355, 511875, 515970, 522720, 528768, 539000, 543312, 546000, 550368, 557568, 557685, 582400, 588060, 594864, 606375, 609375, 611226, 614250, 619164, 627264, 646800, 650000, 655200, 669222, 672280, 689920, 698880, 705672, 721875, 727650, 731250, 737100, 745472, 756315, 770000, 776160, 780000, 786240, 793881, 806736, 827904, 832000, 838656, 859375, 866250, 873180, 877500, 884520, 900375, 907578, 924000, 931392, 936000, 943488, 960400, 985600, 995085, 998400, 1031250, 1039500, 1047816, 1053000, 1061424, 1064960, 1071875, 1080450, 1100000, 1108800, 1123200, 1152480, 1178793, 1182720, 1184625, 1194102, 1198080, 1229312, 1237500, 1247400, 1261568, 1263600, 1277952, 1286250, 1296540, 1320000, 1330560, 1347840, 1372000, 1382976, 1403325, 1408000, 1419264, 1421550, 1437696, 1485000, 1496880, 1516320, 1531250, 1543500, 1555848, 1584000, 1596672, 1617408, 1646400, 1670625, 1683990, 1689600, 1705860, 1750329, 1756160, 1782000, 1796256, 1802240, 1819584, 1837500, 1852200, 1900800, 1960000, 1975680, 2004750, 2020788, 2027520, 2047032, 2083725, 2107392, 2138400, 2162688, 2187500, 2205000, 2222640, 2280960, 2302911, 2352000, 2370816, 2405700, 2433024, 2480625, 2500470, 2508800, 2566080, 2625000, 2646000, 2667168, 2737152, 2800000, 2822400, 2886840, 2953125, 2976750, 3000564, 3010560, 3079296, 3125000, 3150000, 3175200, 3211264, 3247695, 3360000, 3386880, 3464208, 3515625, 3543750, 3572100, 3584000, 3612672, 3750000, 3780000, 3810240, 3897234, 4000000, 4032000, 4064256, 4218750, 4252500, 4286520, 4300800, 4500000, 4536000, 4572288, 4587520, 4800000, 4822335, 4838400, 5062500, 5103000, 5120000, 5143824, 5160960, 5400000, 5443200, 5505024, 5740875, 5760000, 5786802, 5806080, 6075000, 6123600, 6144000, 6193152, 6480000, 6531840, 6553600, 6834375, 6889050, 6912000, 6967296, 7290000, 7348320, 7372800, 7776000, 7838208, 7864320, 8201250, 8266860, 8294400, 8388608, 8748000, 8817984, 8847360, 9331200, 9437184, 9841500, 9920232, 9953280, 10497600, 10616832, 11160261, 11197440, 11809800, 11943936, 12597120, 13286025, 13436928, 14171760, 15116544, 15943230, 17006112, 19131876```

Some figures :

```The biggest descendant number : 3^33 = 5.559.060.566.555.523 (parent 99)

Total Descendants 546.986
```

## AutoHotkey

It is based on the same logic as the Python script.

I seem that the use of an associative array is a little bit slower than the use of a simple array combined with the 'Sort' command, even if the 'Sort' command pumps 85% of the processing time.

`#Warn#SingleInstance force#NoEnv            ; Recommended for performance and compatibility with future AutoHotkey releases.SendMode Input    ; Recommended for new scripts due to its superior speed and reliability.SetBatchLines, -1SetFormat, IntegerFast, D MaxPrime    = 99		; upper bound for the prime factorsMaxAncestor = 99		; greatest parent number Descendants := [] Primes := GetPrimes(MaxPrime)Exclusions := Primes.Clone()Exclusions.Insert(4) if A_Is64bitOS{	Loop, % MaxAncestor		Descendants.Insert({}) 	for i, Prime in Primes	{		Descendants[Prime, Prime] := 0 		for Parent, Children in Descendants		{			if ((Sum := Parent+Prime) > MaxAncestor)				break 			for pr in Children				Descendants[Sum, pr*Prime] := 0		}	} 	for i, v in Exclusions		Descendants[v].Remove(v, "")}else{	Loop, % MaxAncestor		Descendants.Insert([]) 	for i, Prime in Primes	{		Descendants[Prime].Insert(Prime) 		for Parent, Children in Descendants		{			if ((Sum := Parent+Prime) > MaxAncestor)				break 			for j, pr in Children				Descendants[Sum].Insert(pr*Prime)		}	} 	for i, v in Exclusions		Descendants[v].Remove()} if (MaxAncestor > MaxPrime)	Primes := GetPrimes(MaxAncestor) IfExist, %A_ScriptName%.txt	FileDelete, %A_ScriptName%.txt ;-------------------------------------------------------; Arrays :; Integer keys are stored using the native integer type; 32bit key max = 2.147.483.647; 64bit key max = 9.223.372.036.854.775.807;-------------------------------------------------------Tot_desc = 0for Parent, Children in Descendants{	ls_desc =	if A_Is64bitOS	{		nb_desc = 0		for pr in Children			ls_desc .= ", " pr, nb_desc++		ls_desc := LTrim(ls_desc, ", ")	}	else	{		nb_desc := Children.MaxIndex()		for i, pr in Children			ls_desc .= "," pr		ls_desc := LTrim(ls_desc, ",") 		Sort, ls_desc, N D`,		StringReplace, ls_desc, ls_desc, `,,`,%A_Space%, All	} 	ls_anc =	nb_anc := GetAncestors(ls_anc, Parent)	ls_anc := LTrim(ls_anc, ", ") 	FileAppend, % "[" Parent "] Level: " nb_anc "`r`nAncestors: " (nb_anc ? ls_anc : "None") "`r`n"				 , %A_ScriptName%.txt 	if nb_desc	{		Tot_desc += nb_desc		FileAppend, % "Descendants: " nb_desc "`r`n" ls_desc "`r`n`r`n", %A_ScriptName%.txt	}	else		FileAppend, % "Descendants: None`r`n`r`n", %A_ScriptName%.txt} FileAppend, % "Total descendants " Tot_desc, %A_ScriptName%.txtreturn GetAncestors(ByRef _lsAnc, _child){	global Primes 	lChild := _child	lIndex := lParent := 0 	while lChild > 1	{		lPrime := Primes[++lIndex]		while !mod(lChild, lPrime)			lChild //= lPrime, lParent += lPrime	} 	if (lParent = _child or _child = 1)		return 0 	_lsAnc := ", " lParent _lsAnc	li := GetAncestors(_lsAnc, lParent)	return ++li} GetPrimes(_maxPrime=0, _nbrPrime=0){	lPrimes := [] 	if (_maxPrime >= 2 or _nbrPrime >= 1)	{		lPrimes.Insert(2)		lValue = 1 		while (lValue += 2) <= _maxPrime or lPrimes.MaxIndex() < _nbrPrime		{			lMaxPrime := Floor(Sqrt(lValue)) 			for lKey, lPrime in lPrimes			{				if (lPrime > lMaxPrime)		; if prime divisor is greater than Floor(Sqrt(lValue))				{					lPrimes.Insert(lValue)					break				} 				if !Mod(lValue, lPrime)					break			}		}	} 	return lPrimes}`

## C

### Full Approach

You can decompose all the numbers from 1 to 333 (5.559.060.566.555.523).

This solution can take a while.

The InsertChild function is replaced by the AppendChild function which appends directly the child as the new last item in the list.

`#include <math.h>#include <stdio.h>#include <stdlib.h>#include <string.h> #define MAXPRIME 99						// upper bound for the prime factors#define MAXPARENT 99					// greatest parent number#define NBRPRIMES 30					// max number of prime factors#define NBRANCESTORS 10					// max number of parent's ancestors FILE *FileOut;char format[] = ", %lld"; int Primes[NBRPRIMES];					// table of the prime factorsint iPrimes;							// max index of the prime factor table short Ancestors[NBRANCESTORS];			// table of the parent's ancestors struct Children {	long long Child;	struct Children *pNext;};struct Children *Parents[MAXPARENT+1][2];	// table pointing to the root and to the last descendants (per parent)int CptDescendants[MAXPARENT+1];			// counter table of the descendants (per parent)long long MaxDescendant = (long long) pow(3.0, 33.0);	// greatest descendant number short GetParent(long long child);struct Children *AppendChild(struct Children *node, long long child);short GetAncestors(short child);void PrintDescendants(struct Children *node);int GetPrimes(int primes[], int maxPrime); int main(){	long long Child;	short i, Parent, Level;	int TotDesc = 0; 	if ((iPrimes = GetPrimes(Primes, MAXPRIME)) < 0)		return 1; 	for (Child = 1; Child <= MaxDescendant; Child++)	{		if (Parent = GetParent(Child))		{			Parents[Parent][1] = AppendChild(Parents[Parent][1], Child);			if (Parents[Parent][0] == NULL)				Parents[Parent][0] = Parents[Parent][1];			CptDescendants[Parent]++;		}	} 	if (MAXPARENT > MAXPRIME)		if (GetPrimes(Primes, MAXPARENT) < 0)			return 1; 	if (fopen_s(&FileOut, "Ancestors.txt", "w"))		return 1; 	for (Parent = 1; Parent <= MAXPARENT; Parent++)	{		Level = GetAncestors(Parent); 		fprintf(FileOut, "[%d] Level: %d\n", Parent, Level); 		if (Level)		{			fprintf(FileOut, "Ancestors: %d", Ancestors[0]); 			for (i = 1; i < Level; i++)				fprintf(FileOut, ", %d", Ancestors[i]);		}		else			fprintf(FileOut, "Ancestors: None"); 		if (CptDescendants[Parent])		{			fprintf(FileOut, "\nDescendants: %d\n", CptDescendants[Parent]);			strcpy_s(format, "%lld");			PrintDescendants(Parents[Parent][0]);			fprintf(FileOut, "\n");		}		else			fprintf(FileOut, "\nDescendants: None\n"); 		fprintf(FileOut, "\n");		TotDesc += CptDescendants[Parent];	} 	fprintf(FileOut, "Total descendants %d\n\n", TotDesc);	if (fclose(FileOut))		return 1; 	return 0;} short GetParent(long long child){	long long Child = child;	short Parent = 0;	short Index = 0; 	while (Child > 1 && Parent <= MAXPARENT)	{		if (Index > iPrimes)			return 0; 		while (Child % Primes[Index] == 0)		{			Child /= Primes[Index];			Parent += Primes[Index];		} 		Index++;	} 	if (Parent == child || Parent > MAXPARENT || child == 1)		return 0; 	return Parent;} struct Children *AppendChild(struct Children *node, long long child){	static struct Children *NodeNew; 	if (NodeNew = (struct Children *) malloc(sizeof(struct Children)))	{		NodeNew->Child = child;		NodeNew->pNext = NULL;		if (node != NULL)			node->pNext = NodeNew;	} 	return NodeNew;} short GetAncestors(short child){	short Child = child;	short Parent = 0;	short Index = 0; 	while (Child > 1)	{		while (Child % Primes[Index] == 0)		{			Child /= Primes[Index];			Parent += Primes[Index];		} 		Index++;	} 	if (Parent == child || child == 1)		return 0; 	Index = GetAncestors(Parent); 	Ancestors[Index] = Parent;	return ++Index;} void PrintDescendants(struct Children *node){	static struct Children *NodeCurr;	static struct Children *NodePrev; 	NodeCurr = node;	NodePrev = NULL;	while (NodeCurr)	{		fprintf(FileOut, format, NodeCurr->Child);		strcpy_s(format, ", %lld");		NodePrev = NodeCurr;		NodeCurr = NodeCurr->pNext;		free(NodePrev);	} 	return;} int GetPrimes(int primes[], int maxPrime){	if (maxPrime < 2)		return -1; 	int Index = 0, Value = 1;	int Max, i; 	primes[0] = 2; 	while ((Value += 2) <= maxPrime)	{		Max = (int) floor(sqrt((double) Value)); 		for (i = 0; i <= Index; i++)		{			if (primes[i] > Max)			{				if (++Index >= NBRPRIMES)					return -1; 				primes[Index] = Value;				break;			} 			if (Value % primes[i] == 0)				break;		}	} 	return Index;}`

### Optimized Approach

You sum the prime factors from the Prime factor table and you calculate the products.

The sums are the ancestors, the products are the descendants.

It is based on the same logic as the Python script.

`#include <math.h>#include <stdio.h>#include <stdlib.h>#include <string.h> #define MAXPRIME 99						// upper bound for the prime factors#define MAXPARENT 99					// greatest parent number#define NBRPRIMES 30					// max number of prime factors#define NBRANCESTORS 10					// max number of parent's ancestors FILE *FileOut;char format[] = ", %lld"; int Primes[NBRPRIMES];					// table of the prime factorsint iPrimes;							// max index of the prime factor table short Ancestors[NBRANCESTORS];			// table of the parent's ancestors struct Children {	long long Child;	struct Children *pLower;	struct Children *pHigher;};struct Children *Parents[MAXPARENT+1];	// table pointing to the root descendants (per parent)int CptDescendants[MAXPARENT+1];		// counter table of the descendants (per parent) void InsertPreorder(struct Children *node, short sum, int prime);struct Children *InsertChild(struct Children *node, long long child);void RemoveFalseChildren();short GetAncestors(short child);void PrintDescendants(struct Children *node);int GetPrimes(int primes[], int maxPrime); int main(){	short i, Parent, Sum, Level;	int Prime;	int TotDesc = 0;	int MidPrime; 	if ((iPrimes = GetPrimes(Primes, MAXPRIME)) < 0)		return 1; 	MidPrime = Primes[iPrimes] / 2; 	for (i = iPrimes; i >= 0; i--)	{		Prime = Primes[i];		Parents[Prime] = InsertChild(Parents[Prime], Prime);		CptDescendants[Prime]++; 		if (Prime > MidPrime)			continue; 		for (Parent = 1; Parent <= MAXPARENT; Parent++)		{			if ((Sum = Parent+Prime) > MAXPARENT)				break; 			if (Parents[Parent])			{				InsertPreorder(Parents[Parent], Sum, Prime);				CptDescendants[Sum] += CptDescendants[Parent];			}		}	} 	RemoveFalseChildren(); 	if (MAXPARENT > MAXPRIME)		if (GetPrimes(Primes, MAXPARENT) < 0)			return 1; 	if (fopen_s(&FileOut, "Ancestors.txt", "w"))		return 1; 	for (Parent = 1; Parent <= MAXPARENT; Parent++)	{		Level = GetAncestors(Parent); 		fprintf(FileOut, "[%d] Level: %d\n", Parent, Level); 		if (Level)		{			fprintf(FileOut, "Ancestors: %d", Ancestors[0]); 			for (i = 1; i < Level; i++)				fprintf(FileOut, ", %d", Ancestors[i]);		}		else			fprintf(FileOut, "Ancestors: None"); 		if (CptDescendants[Parent])		{			fprintf(FileOut, "\nDescendants: %d\n", CptDescendants[Parent]);			strcpy_s(format, "%lld");			PrintDescendants(Parents[Parent]);			fprintf(FileOut, "\n");		}		else			fprintf(FileOut, "\nDescendants: None\n"); 		fprintf(FileOut, "\n");		TotDesc += CptDescendants[Parent];	} 	fprintf(FileOut, "Total descendants %d\n\n", TotDesc); 	if (fclose(FileOut))		return 1; 	return 0;} void InsertPreorder(struct Children *node, short sum, int prime){	Parents[sum] = InsertChild(Parents[sum], node->Child * prime); 	if (node->pLower)		InsertPreorder(node->pLower, sum, prime); 	if (node->pHigher)		InsertPreorder(node->pHigher, sum, prime);} struct Children *InsertChild(struct Children *node, long long child){	if (node)	{		if (child <= node->Child)			node->pLower = InsertChild(node->pLower, child);		else			node->pHigher = InsertChild(node->pHigher, child);	}	else	{		if (node = (struct Children *) malloc(sizeof(struct Children)))		{			node->Child = child;			node->pLower = NULL;			node->pHigher = NULL;		}	} 	return node;} void RemoveFalseChildren(){	short i, ex;	int Exclusions[NBRPRIMES+1];		// table of the prime factors + {4}	int iExclusions;					// max index of the exclusion table	struct Children *ptr; 	for (i = 0; i <= iPrimes; i++)		Exclusions[i] = Primes[i]; 	iExclusions = iPrimes + 1;	Exclusions[iExclusions] = 4; 	for (i = 0; i <= iExclusions; i++)	{		ex = Exclusions[i];		ptr = Parents[ex];		Parents[ex] = ptr->pHigher;		CptDescendants[ex]--;		free(ptr);	}} short GetAncestors(short child){	short Child = child;	short Parent = 0;	short Index = 0; 	while (Child > 1)	{		while (Child % Primes[Index] == 0)		{			Child /= Primes[Index];			Parent += Primes[Index];		} 		Index++;	} 	if (Parent == child || child == 1)		return 0; 	Index = GetAncestors(Parent); 	Ancestors[Index] = Parent;	return ++Index;} void PrintDescendants(struct Children *node){	if (node->pLower)		PrintDescendants(node->pLower); 	fprintf(FileOut, format, node->Child);	strcpy_s(format, ", %lld"); 	if (node->pHigher)		PrintDescendants(node->pHigher); 	free(node);	return;} int GetPrimes(int primes[], int maxPrime){	if (maxPrime < 2)		return -1; 	int Index = 0, Value = 1;	int Max, i; 	primes[0] = 2; 	while ((Value += 2) <= maxPrime)	{		Max = (int) floor(sqrt((double) Value)); 		for (i = 0; i <= Index; i++)		{			if (primes[i] > Max)			{				if (++Index >= NBRPRIMES)					return -1; 				primes[Index] = Value;				break;			} 			if (Value % primes[i] == 0)				break;		}	} 	return Index;}`

## Go

Translation of: Python
`package main import (    "fmt"    "sort") func getPrimes(max int) []int {    if max < 2 {        return []int{}    }    lprimes := []int{2}outer:    for x := 3; x <= max; x += 2 {        for _, p := range lprimes {            if x%p == 0 {                continue outer            }        }        lprimes = append(lprimes, x)    }    return lprimes} func main() {    const maxSum = 99    descendants := make([][]int64, maxSum+1)    ancestors := make([][]int, maxSum+1)    for i := 0; i <= maxSum; i++ {        descendants[i] = []int64{}        ancestors[i] = []int{}    }    primes := getPrimes(maxSum)     for _, p := range primes {        descendants[p] = append(descendants[p], int64(p))        for s := 1; s < len(descendants)-p; s++ {            temp := make([]int64, len(descendants[s]))            for i := 0; i < len(descendants[s]); i++ {                temp[i] = int64(p) * descendants[s][i]            }            descendants[s+p] = append(descendants[s+p], temp...)        }    }     for _, p := range append(primes, 4) {        le := len(descendants[p])        if le == 0 {            continue        }        descendants[p][le-1] = 0        descendants[p] = descendants[p][:le-1]    }    total := 0     for s := 1; s <= maxSum; s++ {        x := descendants[s]        sort.Slice(x, func(i, j int) bool {            return x[i] < x[j]        })        total += len(descendants[s])        index := 0        for ; index < len(descendants[s]); index++ {            if descendants[s][index] > int64(maxSum) {                break            }        }        for _, d := range descendants[s][:index] {            ancestors[d] = append(ancestors[s], s)        }        if (s >= 21 && s <= 45) || (s >= 47 && s <= 73) || (s >= 75 && s < maxSum) {            continue        }        temp := fmt.Sprintf("%v", ancestors[s])        fmt.Printf("%2d: %d Ancestor(s): %-14s", s, len(ancestors[s]), temp)        le := len(descendants[s])        if le <= 10 {            fmt.Printf("%5d Descendant(s): %v\n", le, descendants[s])        } else {            fmt.Printf("%5d Descendant(s): %v\b ...]\n", le, descendants[s][:10])        }    }    fmt.Println("\nTotal descendants", total)}`
Output:
``` 1: 0 Ancestor(s): []                0 Descendant(s): []
2: 0 Ancestor(s): []                0 Descendant(s): []
3: 0 Ancestor(s): []                0 Descendant(s): []
4: 0 Ancestor(s): []                0 Descendant(s): []
5: 0 Ancestor(s): []                1 Descendant(s): [6]
6: 1 Ancestor(s): [5]               2 Descendant(s): [8 9]
7: 0 Ancestor(s): []                2 Descendant(s): [10 12]
8: 2 Ancestor(s): [5 6]             3 Descendant(s): [15 16 18]
9: 2 Ancestor(s): [5 6]             4 Descendant(s): [14 20 24 27]
10: 1 Ancestor(s): [7]               5 Descendant(s): [21 25 30 32 36]
11: 0 Ancestor(s): []                5 Descendant(s): [28 40 45 48 54]
12: 1 Ancestor(s): [7]               7 Descendant(s): [35 42 50 60 64 72 81]
13: 0 Ancestor(s): []                8 Descendant(s): [22 56 63 75 80 90 96 108]
14: 3 Ancestor(s): [5 6 9]          10 Descendant(s): [33 49 70 84 100 120 128 135 144 162]
15: 3 Ancestor(s): [5 6 8]          12 Descendant(s): [26 44 105 112 125 126 150 160 180 192 ...]
16: 3 Ancestor(s): [5 6 8]          14 Descendant(s): [39 55 66 98 140 168 189 200 225 240 ...]
17: 0 Ancestor(s): []               16 Descendant(s): [52 88 99 147 175 210 224 250 252 300 ...]
18: 3 Ancestor(s): [5 6 8]          19 Descendant(s): [65 77 78 110 132 196 280 315 336 375 ...]
19: 0 Ancestor(s): []               22 Descendant(s): [34 104 117 165 176 198 245 294 350 420 ...]
20: 3 Ancestor(s): [5 6 9]          26 Descendant(s): [51 91 130 154 156 220 264 297 392 441 ...]
46: 3 Ancestor(s): [7 10 25]       557 Descendant(s): [129 205 246 493 518 529 740 806 888 999 ...]
74: 5 Ancestor(s): [5 6 8 16 39]  6336 Descendant(s): [213 469 670 793 804 1333 1342 1369 1534 2014 ...]
99: 1 Ancestor(s): [17]          38257 Descendant(s): [194 1869 2225 2670 2848 3204 3237 4029 4565 5037 ...]

Total descendants 546986
```

## J

### Definition of terms

For this task, based on extensive discussion and examination of the early example implementations, these definitions might be sufficient:

An "allocation" P of N is a list of primes whose sum is N which includes prime number P. (For example 5 7, 2 5 5, and 2 2 3 5 are each examples of the 5 of 12 allocation.)

The "family" of N is all distinct products of allocations P of N. (So we can think of our lists as being capable of producing sets: if different sequences of primes produced the same product we still would only count that product once.)

The "descendants" or "direct descendants" of N are all members of its family excluding N itself. (As N could be in its own family if it is prime or if N is 4.)

A "deallocation" of N is the sum of its prime factorization. (For example, the deallocation of 12 is 2+2+3 or 7.)

A "family tree" of N is all the distinct values resulting from applying deallocation inductively (or iteratively or recursively or repeatedly). (For example, the family tree of 15 is 15 8 6 5 and the family tree of 12 is 12 7. Note that this means that the smallest member of a "family tree" is always a prime.)

The "ancestors" of N are all members of its family tree excluding itself.

The "total" of a set of numbers X is the number of members in that set. In other words, the "total" of {5,6} is 2. (So we use the word "sum" instead of "total" when talking about addition in the context of this exercise, because this exercise requires that sort of doublethink.)

"Print" means "calculate and store somewhere".

### Implementation I

`require'strings files' family=:3 :0 M.  if. 2>y do.    i.0   NB. no primes less than 2  else.    p=. i.&.(p:inv) y    (y#~1 p:y),~.;p (* family)&.>y-p  end.) familytree=: +/@q:^:a: ::(''"_) descendants=: family -. ]ancestors=: 1 }. familytreelevel=: #@ancestors"0 taskfmt=:'None'"_^:(0=#)@rplc&(' ';', ')@": task1=:3 :0  text=. '[',(":y),'] Level: ',(":level y),LF  text=. text,'Ancestors: ',(taskfmt /:~ancestors y),LF  if. #descendants y do.    text=. text,'Descendants: ',(":#descendants y),LF    text=. text,(taskfmt /:~descendants y),LF  else.    text=. text,'Descendants: None',LF  end.  text=. text,LF) task=:3 :0  tot=. 'Total descendants ',(":#@; descendants&.> 1+i.y),LF  ((;task1&.>1+i.y),tot) fwrite jpath '~user/temp/Ancestors.txt') task 99`

If you want to inspect individual results, that's fairly straightforward.

The produced text file comes not from the task description but from Implementation II (except omitting the CR at line end - you can use unix/osx/linux/cygwin's `diff -bw` to compare the generated files).

Can we assume you use the '9!:11 +20' function in your profile? Otherwise the big values are shown in scientific notation.

### Some examples

`   #;descendants&.>1+i.99546986   level 463   ancestors 4625 10 7   #descendants 46557   descendants 18512 576 480 336 400 648 280 132 540 196 78 378 450 110 729 315 375 65 77   level 183   ancestors 188 6 5   #descendants 1819`

### Implementation II

Translation of: Python

After reading the "Learning J" documentation up to chapter 9 + some additional verbs, I can post my first J script.

The script is based on the same logic as the Python script and therefore on the original task description.

However, I use the 'FamilyTree' function of implementation I, as the 'getancestors' function.

Furthermore, the script produces the full report in a '.txt' file which can easily be compared with the output of some of the other languages. In Windows : `fc /N /L`

`getdescendants=: 3 : 0  dd=: (<(>y{dd),y)y}dd  y getproducts"0 >:i.maxsum-y) getproducts=: 4 : 'dd=: (<(>(x+y){dd),x*(>y{dd))(x+y)}dd' delfalsechildren=: 3 : 'dd=: ((}:&.>)y{dd)y}dd' report=: 3 : 0  ac=. getancestors y  if. (level=. #ac) = 0 do.    ls=. 'None'  else.    ls=. (' ';', ') stringreplace ":ac  end.  line=. '[',(":y),'] Level: ',(":level),CR,LF,'Ancestors: ',ls,CR,LF  if. (nb=. #>y{dd) = 0 do.    line=. line,'Descendants: ','None',CR,LF,CR,LF  else.    ls=. (' ';', ') stringreplace ":/:~>y{dd    line=. line,'Descendants: ',(":nb),CR,LF,ls,CR,LF,CR,LF  end.  line fappend file) getancestors=: |[email protected]:(1}.+/@:q:^:a: ::(''"_)) main=: 3 : 0  if. (pp1=. 9!:10 '') < 20 do. (9!:11) 20 end.  '' fwrite file  maxsum=: y  dd=: (maxsum+1)\$a:  primes=. i.&.(p:inv)maxsum+1  getdescendants"0 primes  delfalsechildren"0 primes,4  report"0 >:i.maxsum  ('Total descendants ',":+/#&>dd) fappend file  if. (pp2=. 9!:10 '') ~: pp1 do. (9!:11) pp1 end.) file=: jpath '~user/temp/Ancestors.ijs.txt'main 99`

## Julia

Translation of: Go
`using Primes function ancestraldecendants(maxsum)    aprimes = primes(maxsum)    descendants = [Vector{Int}() for _ in 1:maxsum + 1]    ancestors = [Vector{Int}() for _ in 1:maxsum + 1]    for p in aprimes        push!(descendants[p + 1], p)        foreach(s -> append!(descendants[s + p], [p * pr for pr in descendants[s]]),            2:length(descendants) - p)    end    foreach(p -> pop!(descendants[p + 1]), vcat(aprimes, [4]))    total = 0    for s in 1:maxsum        sort!(descendants[s + 1])        dstlen = length(descendants[s + 1])        total += dstlen        idx = findfirst(x -> x > maxsum, descendants[s + 1])        idx  = (idx == nothing) ? dstlen : idx - 1        foreach(d -> ancestors[d] = vcat(ancestors[s + 1], [s]), descendants[s + 1][1:idx])        if s in vcat(collect(0:20), 46, 74, 99)            print(lpad(s, 3), ":", lpad("\$(length(ancestors[s + 1]))", 2))            print(" Ancestor(s):", rpad("\$(ancestors[s + 1])", 18))            print(lpad("\$(length(descendants[s + 1]))", 5), " Descendant(s): ")            println(rpad(dstlen <= 10 ? "\$(descendants[s + 1])" : "\$(descendants[s + 1][1:10])\b, ...]", 40))        end    end    print("Total descendants: ", total)end ancestraldecendants(99) `
Output:
```
1: 0 Ancestor(s):Int64[]               0 Descendant(s): Int64[]
2: 0 Ancestor(s):Int64[]               0 Descendant(s): Int64[]
3: 0 Ancestor(s):Int64[]               0 Descendant(s): Int64[]
4: 0 Ancestor(s):Int64[]               0 Descendant(s): Int64[]
5: 1 Ancestor(s):[5]                   1 Descendant(s): [6]
6: 0 Ancestor(s):Int64[]               2 Descendant(s): [8, 9]
7: 1 Ancestor(s):[6]                   2 Descendant(s): [10, 12]
8: 1 Ancestor(s):[6]                   3 Descendant(s): [15, 16, 18]
9: 2 Ancestor(s):[6, 7]                4 Descendant(s): [14, 20, 24, 27]
10: 0 Ancestor(s):Int64[]               5 Descendant(s): [21, 25, 30, 32, 36]
11: 2 Ancestor(s):[6, 7]                5 Descendant(s): [28, 40, 45, 48, 54]
12: 0 Ancestor(s):Int64[]               7 Descendant(s): [35, 42, 50, 60, 64, 72, 81]
13: 3 Ancestor(s):[6, 7, 9]             8 Descendant(s): [22, 56, 63, 75, 80, 90, 96, 108]
14: 2 Ancestor(s):[6, 8]               10 Descendant(s): [33, 49, 70, 84, 100, 120, 128, 135, 144, 162]
15: 2 Ancestor(s):[6, 8]               12 Descendant(s): [26, 44, 105, 112, 125, 126, 150, 160, 180, 192, ...]
16: 0 Ancestor(s):Int64[]              14 Descendant(s): [39, 55, 66, 98, 140, 168, 189, 200, 225, 240, ...]
17: 2 Ancestor(s):[6, 8]               16 Descendant(s): [52, 88, 99, 147, 175, 210, 224, 250, 252, 300, ...]
18: 0 Ancestor(s):Int64[]              19 Descendant(s): [65, 77, 78, 110, 132, 196, 280, 315, 336, 375, ...]
19: 3 Ancestor(s):[6, 7, 9]            22 Descendant(s): [34, 104, 117, 165, 176, 198, 245, 294, 350, 420, ...]
20: 1 Ancestor(s):[10]                 26 Descendant(s): [51, 91, 130, 154, 156, 220, 264, 297, 392, 441, ...]
46: 0 Ancestor(s):Int64[]             557 Descendant(s): [129, 205, 246, 493, 518, 529, 740, 806, 888, 999, ...]
74: 4 Ancestor(s):[6, 7, 9, 13]      6336 Descendant(s): [213, 469, 670, 793, 804, 1333, 1342, 1369, 1534, 2014, ...]
99: 0 Ancestor(s):Int64[]           38257 Descendant(s): [194, 1869, 2225, 2670, 2848, 3204, 3237, 4029, 4565, 5037, ...]

Total descendants: 546986

```

## Kotlin

Translation of: Python
`// version 1.1.2 const val MAXSUM = 99 fun getPrimes(max: Int): List<Int> {    if (max < 2) return emptyList<Int>()    val lprimes = mutableListOf(2)    outer@ for (x in 3..max step 2) {        for (p in lprimes) if (x % p == 0) continue@outer        lprimes.add(x)    }    return lprimes} fun main(args: Array<String>) {    val descendants = Array(MAXSUM + 1) { mutableListOf<Long>() }    val ancestors   = Array(MAXSUM + 1) { mutableListOf<Int>() }    val primes = getPrimes(MAXSUM)     for (p in primes) {        descendants[p].add(p.toLong())        for (s in 1 until descendants.size - p) {            val temp = descendants[s + p] + descendants[s].map { p * it }            descendants[s + p] = temp.toMutableList()        }    }     for (p in primes + 4) descendants[p].removeAt(descendants[p].lastIndex)    var total = 0     for (s in 1..MAXSUM) {        descendants[s].sort()        total += descendants[s].size                for (d in descendants[s].takeWhile { it <= MAXSUM.toLong() }) {            ancestors[d.toInt()] = (ancestors[s] + s).toMutableList()        }        if (s in 21..45 || s in 47..73 || s in 75 until MAXSUM) continue        print("\${"%2d".format(s)}: \${ancestors[s].size} Ancestor(s): ")        print(ancestors[s].toString().padEnd(18))        print("\${"%5d".format(descendants[s].size)} Descendant(s): ")        println("\${descendants[s].joinToString(", ", "[", "]", 10)}")            }     println("\nTotal descendants \$total")  }`
Output:
``` 1: 0 Ancestor(s): []                    0 Descendant(s): []
2: 0 Ancestor(s): []                    0 Descendant(s): []
3: 0 Ancestor(s): []                    0 Descendant(s): []
4: 0 Ancestor(s): []                    0 Descendant(s): []
5: 0 Ancestor(s): []                    1 Descendant(s): [6]
6: 1 Ancestor(s): [5]                   2 Descendant(s): [8, 9]
7: 0 Ancestor(s): []                    2 Descendant(s): [10, 12]
8: 2 Ancestor(s): [5, 6]                3 Descendant(s): [15, 16, 18]
9: 2 Ancestor(s): [5, 6]                4 Descendant(s): [14, 20, 24, 27]
10: 1 Ancestor(s): [7]                   5 Descendant(s): [21, 25, 30, 32, 36]
11: 0 Ancestor(s): []                    5 Descendant(s): [28, 40, 45, 48, 54]
12: 1 Ancestor(s): [7]                   7 Descendant(s): [35, 42, 50, 60, 64, 72, 81]
13: 0 Ancestor(s): []                    8 Descendant(s): [22, 56, 63, 75, 80, 90, 96, 108]
14: 3 Ancestor(s): [5, 6, 9]            10 Descendant(s): [33, 49, 70, 84, 100, 120, 128, 135, 144, 162]
15: 3 Ancestor(s): [5, 6, 8]            12 Descendant(s): [26, 44, 105, 112, 125, 126, 150, 160, 180, 192, ...]
16: 3 Ancestor(s): [5, 6, 8]            14 Descendant(s): [39, 55, 66, 98, 140, 168, 189, 200, 225, 240, ...]
17: 0 Ancestor(s): []                   16 Descendant(s): [52, 88, 99, 147, 175, 210, 224, 250, 252, 300, ...]
18: 3 Ancestor(s): [5, 6, 8]            19 Descendant(s): [65, 77, 78, 110, 132, 196, 280, 315, 336, 375, ...]
19: 0 Ancestor(s): []                   22 Descendant(s): [34, 104, 117, 165, 176, 198, 245, 294, 350, 420, ...]
20: 3 Ancestor(s): [5, 6, 9]            26 Descendant(s): [51, 91, 130, 154, 156, 220, 264, 297, 392, 441, ...]
46: 3 Ancestor(s): [7, 10, 25]         557 Descendant(s): [129, 205, 246, 493, 518, 529, 740, 806, 888, 999, ...]
74: 5 Ancestor(s): [5, 6, 8, 16, 39]  6336 Descendant(s): [213, 469, 670, 793, 804, 1333, 1342, 1369, 1534, 2014, ...]
99: 1 Ancestor(s): [17]              38257 Descendant(s): [194, 1869, 2225, 2670, 2848, 3204, 3237, 4029, 4565, 5037, ...]

Total descendants 546986
```

## Perl

Translation of: Perl 6
Library: ntheory
`use List::Util qw(sum uniq);use ntheory qw(nth_prime); my \$max = 99;my %tree; sub allocate {    my(\$n, \$i, \$sum,, \$prod) = @_;    \$i //= 0; \$sum //= 0; \$prod //= 1;     for my \$k (0..\$max) {        next if \$k < \$i;        my \$p = nth_prime(\$k+1);        if ((\$sum + \$p) <= \$max) {            allocate(\$n, \$k, \$sum + \$p, \$prod * \$p);        } else {            last if \$sum == \$prod;            \$tree{\$sum}{descendants}{\$prod} = 1;            \$tree{\$prod}{ancestor} = [uniq \$sum, @{\$tree{\$sum}{ancestor}}] unless \$prod > \$max || \$sum == 0;            last;        }    }} sub abbrev { # abbreviate long lists to first and last 5 elements    my(@d) = @_;    return @d if @d < 11;    @d[0 .. 4], '...', @d[-5 .. -1];} allocate(\$_) for 1 .. \$max; for (1 .. 15, 46, \$max) {    printf "%2d, %2d Ancestors: %-15s", \$_, (scalar uniq @{\$tree{\$_}{ancestor}}),        '[' . join(' ',uniq @{\$tree{\$_}{ancestor}}) . ']';    my \$dn = 0; my \$dl = '';    if (\$tree{\$_}{descendants}) {        \$dn = keys %{\$tree{\$_}{descendants}};        \$dl = join ' ', abbrev(sort { \$a <=> \$b } keys %{\$tree{\$_}{descendants}});    }    printf "%5d Descendants: %s", \$dn, "[\$dl]\n";} map { for my \$k (keys %{\$tree{\$_}{descendants}}) { \$total += \$tree{\$_}{descendants}{\$k} } } 1..\$max;print "\nTotal descendants: \$total\n";`
Output:
``` 1,  0 Ancestors: [],                0 Descendants: []
2,  0 Ancestors: [],                0 Descendants: []
3,  0 Ancestors: [],                0 Descendants: []
4,  0 Ancestors: [],                0 Descendants: []
5,  0 Ancestors: [],                1 Descendants: [6]
6,  1 Ancestors: [5],               2 Descendants: [8 9]
7,  0 Ancestors: [],                2 Descendants: [10 12]
8,  2 Ancestors: [5 6],             3 Descendants: [15 16 18]
9,  2 Ancestors: [5 6],             4 Descendants: [14 20 24 27]
10,  1 Ancestors: [7],               5 Descendants: [21 25 30 32 36]
11,  0 Ancestors: [],                5 Descendants: [28 40 45 48 54]
12,  1 Ancestors: [7],               7 Descendants: [35 42 50 60 64 72 81]
13,  0 Ancestors: [],                8 Descendants: [22 56 63 75 80 90 96 108]
14,  3 Ancestors: [5 6 9],          10 Descendants: [33 49 70 84 100 120 128 135 144 162]
15,  3 Ancestors: [5 6 8],          12 Descendants: [26 44 105 112 125 ... 160 180 192 216 243]
46,  3 Ancestors: [7 10 25],       557 Descendants: [129 205 246 493 518 ... 14171760 15116544 15943230 17006112 19131876]
99,  1 Ancestors: [17],          38257 Descendants: [194 1869 2225 2670 2848 ... 3904305912313344 4117822641892980 4392344151352512 4941387170271576 5559060566555523]

Total descendants: 546986```

## Perl 6

Works with: Rakudo version 2018.11
`my \$max = 99;my @primes = (2 .. \$max).race(:16batch).grep: *.is-prime;my %tree;(1..\$max).race(:16batch).map: {    %tree{\$_}<ancestor> = ();    %tree{\$_}<descendants> = {};};  sub allocate (\$n, \$i = 0, \$sum = 0, \$prod = 1) {    return if \$n < 4;    for @primes.kv -> \$k, \$p {        next if \$k < \$i;        if (\$sum + \$p) <= \$n {            allocate(\$n, \$k, \$sum + \$p, \$prod * \$p);        } else {            last if \$sum == \$prod;            %tree{\$sum}<descendants>{\$prod} = True;            last if \$prod > \$max;            %tree{\$prod}<ancestor> = %tree{\$sum}<ancestor> (|) \$sum;            last;        }    }} # abbreviate long lists to first and last 5 elementssub abbrev (@d) { @d < 11 ?? @d !! ( @d.head(5), '...', @d.tail(5) ) } my @print = flat 1 .. 15, 46, 74, \$max; (1 .. \$max).map: -> \$term {    allocate(\$term);     if \$term == any( @print )  # print some representative lines    {        my \$dn = +%tree{\$term}<descendants> // 0;        my \$dl = abbrev(%tree{\$term}<descendants>.keys.sort( +*) // ());        printf "%2d, %2d Ancestors: %-14s %5d Descendants: %s\n",          \$term, %tree{\$term}<ancestor>,          "[{ %tree{\$term}<ancestor>.keys.sort: +* }],", \$dn, "[\$dl]";    }} say "\nTotal descendants: ",  sum (1..\$max).race(:16batch).map({ +%tree{\$_}<descendants> });`
Output:
``` 1,  0 Ancestors: [],                0 Descendants: []
2,  0 Ancestors: [],                0 Descendants: []
3,  0 Ancestors: [],                0 Descendants: []
4,  0 Ancestors: [],                0 Descendants: []
5,  0 Ancestors: [],                1 Descendants: [6]
6,  1 Ancestors: [5],               2 Descendants: [8 9]
7,  0 Ancestors: [],                2 Descendants: [10 12]
8,  2 Ancestors: [5 6],             3 Descendants: [15 16 18]
9,  2 Ancestors: [5 6],             4 Descendants: [14 20 24 27]
10,  1 Ancestors: [7],               5 Descendants: [21 25 30 32 36]
11,  0 Ancestors: [],                5 Descendants: [28 40 45 48 54]
12,  1 Ancestors: [7],               7 Descendants: [35 42 50 60 64 72 81]
13,  0 Ancestors: [],                8 Descendants: [22 56 63 75 80 90 96 108]
14,  3 Ancestors: [5 6 9],          10 Descendants: [33 49 70 84 100 120 128 135 144 162]
15,  3 Ancestors: [5 6 8],          12 Descendants: [26 44 105 112 125 ... 160 180 192 216 243]
46,  3 Ancestors: [7 10 25],       557 Descendants: [129 205 246 493 518 ... 14171760 15116544 15943230 17006112 19131876]
74,  5 Ancestors: [5 6 8 16 39],  6336 Descendants: [213 469 670 793 804 ... 418414128120 446308403328 470715894135 502096953744 564859072962]
99,  1 Ancestors: [17],          38257 Descendants: [194 1869 2225 2670 2848 ... 3904305912313344 4117822641892980 4392344151352512 4941387170271576 5559060566555523]

Total descendants: 546986```

## Phix

Translation of: Go
`constant maxSum = 99 function getPrimes()    sequence primes = {2}    for x=3 to maxSum by 2 do        bool zero = false        for i=1 to length(primes) do            if mod(x,primes[i]) == 0 then                zero = true                exit            end if        end for        if not zero then            primes = append(primes, x)        end if    end for    return primesend function function stringify(sequence s)    for i=1 to length(s) do        s[i] = sprintf("%d",s[i])    end for     return send function procedure main()atom t0 = time()integer p    sequence descendants = repeat({},maxSum+1),             ancestors = repeat({},maxSum+1),             primes = getPrimes()     for i=1 to length(primes) do        p = primes[i]        descendants[p] = append(descendants[p], p)        for s=1 to length(descendants)-p do            descendants[s+p] &= sq_mul(descendants[s], p)        end for    end for     p = 4    for i=0 to length(primes) do        if i>0 then p = primes[i] end if        if length(descendants[p])!=0 then            descendants[p] = descendants[p][1..\$-1]        end if    end for     integer total = 0     for s=1 to maxSum do        sequence x = sort(descendants[s])        total += length(x)        for i=1 to length(x) do            atom d = x[i]            if d>maxSum then exit end if            ancestors[d] &= append(ancestors[s], s)        end for        if s<26 or find(s,{46,74,99}) then              sequence d = ancestors[s]            integer l = length(d)            string sp = iff(l=1?" ":"s")            d = stringify(d)            printf(1,"%2d: %d Ancestor%s: [%-14s", {s, l, sp, join(d)&"]"})            d = sort(descendants[s])            l = length(d)            sp = iff(l=1?" ":"s")            if l<10 then                d = stringify(d)            else                d[4..-4] = {0}                d = stringify(d)                d[4] = "..."            end if            printf(1,"%5d Descendant%s: [%s]\n", {l, sp, join(d)})        end if    end for    printf(1,"\nTotal descendants %d\n", total)    ?elapsed(time()-t0)                         -- < 1s    ?elapsed(5559060566555523/4_000_000_000)    -- > 16 daysend proceduremain()`
Output:
``` 1: 0 Ancestors: []                 0 Descendants: []
2: 0 Ancestors: []                 0 Descendants: []
3: 0 Ancestors: []                 0 Descendants: []
4: 0 Ancestors: []                 0 Descendants: []
5: 0 Ancestors: []                 1 Descendant : [6]
6: 1 Ancestor : [5]                2 Descendants: [8 9]
7: 0 Ancestors: []                 2 Descendants: [10 12]
8: 2 Ancestors: [5 6]              3 Descendants: [15 16 18]
9: 2 Ancestors: [5 6]              4 Descendants: [14 20 24 27]
10: 1 Ancestor : [7]                5 Descendants: [21 25 30 32 36]
11: 0 Ancestors: []                 5 Descendants: [28 40 45 48 54]
12: 1 Ancestor : [7]                7 Descendants: [35 42 50 60 64 72 81]
13: 0 Ancestors: []                 8 Descendants: [22 56 63 75 80 90 96 108]
14: 3 Ancestors: [5 6 9]           10 Descendants: [33 49 70 ... 135 144 162]
15: 3 Ancestors: [5 6 8]           12 Descendants: [26 44 105 ... 192 216 243]
16: 3 Ancestors: [5 6 8]           14 Descendants: [39 55 66 ... 270 288 324]
17: 0 Ancestors: []                16 Descendants: [52 88 99 ... 405 432 486]
18: 3 Ancestors: [5 6 8]           19 Descendants: [65 77 78 ... 576 648 729]
19: 0 Ancestors: []                22 Descendants: [34 104 117 ... 810 864 972]
20: 3 Ancestors: [5 6 9]           26 Descendants: [51 91 130 ... 1215 1296 1458]
21: 2 Ancestors: [7 10]            30 Descendants: [38 68 195 ... 1728 1944 2187]
22: 1 Ancestor : [13]              35 Descendants: [57 85 102 ... 2430 2592 2916]
23: 0 Ancestors: []                39 Descendants: [76 136 153 ... 3645 3888 4374]
24: 3 Ancestors: [5 6 9]           46 Descendants: [95 114 119 ... 5184 5832 6561]
25: 2 Ancestors: [7 10]            52 Descendants: [46 152 171 ... 7290 7776 8748]
46: 3 Ancestors: [7 10 25]        557 Descendants: [129 205 246 ... 15943230 17006112 19131876]
74: 5 Ancestors: [5 6 8 16 39]   6336 Descendants: [213 469 670 ... 470715894135 502096953744 564859072962]
99: 1 Ancestor : [17]           38257 Descendants: [194 1869 2225 ... 4392344151352512 4941387170271576 5559060566555523]

Total descendants 546986
"0.7s"
"16 days, 2 hours, 2 minutes and 45s"
```

The quick test at the end suggests that a 4Ghz chip would take at least 16 days just to count to 5559060566555523, let alone decompose those numbers into prime factors (and throwing away the ones you don't need, probably more like 10 million years), which as requested in the task description obviously demonstrates that the algorithm can be crucial in terms of performance.

## Python

Python is very flexible, concise and effective with lists.

`from __future__ import print_functionfrom itertools import takewhile maxsum = 99 def get_primes(max):    if max < 2:        return []    lprimes = [2]    for x in range(3, max + 1, 2):        for p in lprimes:            if x % p == 0:                break        else:            lprimes.append(x)    return lprimes descendants = [[] for _ in range(maxsum + 1)]ancestors = [[] for _ in range(maxsum + 1)] primes = get_primes(maxsum) for p in primes:    descendants[p].append(p)    for s in range(1, len(descendants) - p):        descendants[s + p] += [p * pr for pr in descendants[s]] for p in primes + [4]:    descendants[p].pop() total = 0for s in range(1, maxsum + 1):    descendants[s].sort()    for d in takewhile(lambda x: x <= maxsum, descendants[s]):        ancestors[d] = ancestors[s] + [s]    print([s], "Level:", len(ancestors[s]))    print("Ancestors:", ancestors[s] if len(ancestors[s]) else "None")    print("Descendants:", len(descendants[s]) if len(descendants[s]) else "None")    if len(descendants[s]):        print(descendants[s])    print()    total += len(descendants[s]) print("Total descendants", total)`

## Racket

Translation of: Python

I think that this is not anymore a translation of Python, since the 'Python script I' is gone.

The program has a few changes from the versions in other languages. The equation `p*q=p+q` has only one integer solution, so all the ancestor candidates are smaller than the number, except for `4=2+2=2*2`. So we can replace the inecuality by a special case for `4`.

We only show here a few values to be able to compare the output. We also show the total number of ancestors.

We first define a macro to create memorized functions and a few auxiliary functions. In particular `(border list)` transforms a long list in a list with ellipsis.

`#lang racket (define-syntax-rule (define/mem (name args ...) body ...)  (begin    (define cache (make-hash))    (define (name args ...)      (hash-ref! cache (list args ...) (lambda () body ...))))) (define (take-last x n)  (drop x (- (length x) n))) (define (borders x)  (if (> (length x) 5)    (append (take x 2) '(...) (take-last x 2))    x)) (define (add-tail list x)  (reverse (cons x (reverse list))))`

The main part of the program uses the memorized functions.

` (define/mem (prime? x)  (if (= x 1)    #f    (not (for/or ([p (in-range 2 x)]                  #:break (> (sqr p) x))           (zero? (remainder x p)))))) (define (map* p list)  (map (lambda (x) (* x p)) list)) (define/mem (part-prod x p)  (cond    [(< x 0) '()]    [(zero? x) (list 1)]    [(zero? p) '()]    [(not (prime? p)) (part-prod x (sub1 p))]    [else (append (map* p (part-prod (- x p) p))                  (part-prod x (sub1 p)))])) (define/mem (descendants x)  (if (= x 4)      '()      (sort (part-prod x (sub1 x)) <))) (define/mem (ancestors z)  (let ([tmp (for/first ([x (in-range (sub1 z) 0 -1)]                         #:when (member z (descendants x)))               (add-tail (ancestors x) x))])    (if tmp tmp '()))) (define (show-info x)  (printf "~a " x)  (printf "Ancestors: ~a ~a " (length (ancestors x)) (ancestors x))  (printf "Descendants: ~a ~a " (length (descendants x)) (borders (descendants x)))  (newline)) (define (total-ancestors n)  (for/sum ([x (in-range 1 (add1 n))])    (length (ancestors x)))) (define (total-descendants n)  (for/sum ([x (in-range 1 (add1 n))])    (length (descendants x))))`

Now we display some results.

`#;(for ([x (in-range 1 (add1 99))])    (show-info x))(for ([x (in-range 1 (add1 15))])  (show-info x)) (newline)(show-info 18)(show-info 46)(show-info 99) (newline)(printf "Total ancestors up to 99: ~a\n" (total-ancestors 99))(printf "Total descendants up to 99: ~a\n" (total-descendants 99))`
Output:
```1 Ancestors: 0 () Descendants: 0 ()
2 Ancestors: 0 () Descendants: 0 ()
3 Ancestors: 0 () Descendants: 0 ()
4 Ancestors: 0 () Descendants: 0 ()
5 Ancestors: 0 () Descendants: 1 (6)
6 Ancestors: 1 (5) Descendants: 2 (8 9)
7 Ancestors: 0 () Descendants: 2 (10 12)
8 Ancestors: 2 (5 6) Descendants: 3 (15 16 18)
9 Ancestors: 2 (5 6) Descendants: 4 (14 20 24 27)
10 Ancestors: 1 (7) Descendants: 5 (21 25 30 32 36)
11 Ancestors: 0 () Descendants: 5 (28 40 45 48 54)
12 Ancestors: 1 (7) Descendants: 7 (35 42 ... 72 81)
13 Ancestors: 0 () Descendants: 8 (22 56 ... 96 108)
14 Ancestors: 3 (5 6 9) Descendants: 10 (33 49 ... 144 162)
15 Ancestors: 3 (5 6 8) Descendants: 12 (26 44 ... 216 243)

18 Ancestors: 3 (5 6 8) Descendants: 19 (65 77 ... 648 729)
46 Ancestors: 3 (7 10 25) Descendants: 557 (129 205 ... 17006112 19131876)
99 Ancestors: 1 (17) Descendants: 38257 (194 1869 ... 4941387170271576 5559060566555523)

Total ancestors up to 99: 179
Total descendants up to 99: 546986```

## Sidef

Translation of: Go
`var maxsum = 99var primes = maxsum.primes var descendants = (maxsum+1).of { [] }var ancestors   = (maxsum+1).of { [] } for p in (primes) {    descendants[p] << p    for s in (1 .. descendants.end-p) {        descendants[s + p] << descendants[s].map {|q| p*q }...    }} for p in (primes + [4]) {    descendants[p].pop} var total = 0 for s in (1 .. maxsum) {     descendants[s].sort!     total += (var dsclen = descendants[s].len)    var idx = descendants[s].first_index {|x| x > maxsum }     for d in (descendants[s].slice(0, idx)) {        ancestors[d] = (ancestors[s] + [s])    }     if ((s <= 20) || (s ~~ [46, 74, 99])) {        printf("%2d: %d Ancestor(s): %-15s %5s Descendant(s): %s\n", s,            ancestors[s].len, "[#{ancestors[s].join(' ')}]", descendants[s].len,            dsclen <= 10 ? descendants[s] : "[#{descendants[s].first(10).join(' ')} ...]")    }} say "\nTotal descendants: #{total}"`
Output:
``` 1: 0 Ancestor(s): []                  0 Descendant(s): []
2: 0 Ancestor(s): []                  0 Descendant(s): []
3: 0 Ancestor(s): []                  0 Descendant(s): []
4: 0 Ancestor(s): []                  0 Descendant(s): []
5: 0 Ancestor(s): []                  1 Descendant(s): [6]
6: 1 Ancestor(s): [5]                 2 Descendant(s): [8, 9]
7: 0 Ancestor(s): []                  2 Descendant(s): [10, 12]
8: 2 Ancestor(s): [5 6]               3 Descendant(s): [15, 16, 18]
9: 2 Ancestor(s): [5 6]               4 Descendant(s): [14, 20, 24, 27]
10: 1 Ancestor(s): [7]                 5 Descendant(s): [21, 25, 30, 32, 36]
11: 0 Ancestor(s): []                  5 Descendant(s): [28, 40, 45, 48, 54]
12: 1 Ancestor(s): [7]                 7 Descendant(s): [35, 42, 50, 60, 64, 72, 81]
13: 0 Ancestor(s): []                  8 Descendant(s): [22, 56, 63, 75, 80, 90, 96, 108]
14: 3 Ancestor(s): [5 6 9]            10 Descendant(s): [33, 49, 70, 84, 100, 120, 128, 135, 144, 162]
15: 3 Ancestor(s): [5 6 8]            12 Descendant(s): [26 44 105 112 125 126 150 160 180 192 ...]
16: 3 Ancestor(s): [5 6 8]            14 Descendant(s): [39 55 66 98 140 168 189 200 225 240 ...]
17: 0 Ancestor(s): []                 16 Descendant(s): [52 88 99 147 175 210 224 250 252 300 ...]
18: 3 Ancestor(s): [5 6 8]            19 Descendant(s): [65 77 78 110 132 196 280 315 336 375 ...]
19: 0 Ancestor(s): []                 22 Descendant(s): [34 104 117 165 176 198 245 294 350 420 ...]
20: 3 Ancestor(s): [5 6 9]            26 Descendant(s): [51 91 130 154 156 220 264 297 392 441 ...]
46: 3 Ancestor(s): [7 10 25]         557 Descendant(s): [129 205 246 493 518 529 740 806 888 999 ...]
74: 5 Ancestor(s): [5 6 8 16 39]    6336 Descendant(s): [213 469 670 793 804 1333 1342 1369 1534 2014 ...]
99: 1 Ancestor(s): [17]            38257 Descendant(s): [194 1869 2225 2670 2848 3204 3237 4029 4565 5037 ...]

Total descendants: 546986
```

## Simula

Translation of: Python
`COMMENT cim --memory-pool-size=512 allocate-descendants-to-their-ancestors.sim ;BEGIN      COMMENT ABSTRACT FRAMEWORK CLASSES ;     CLASS ITEM;    BEGIN    END ITEM;     CLASS ITEMLIST;    BEGIN         CLASS ITEMARRAY(N); INTEGER N;        BEGIN REF(ITEM) ARRAY DATA(0:N-1);        END ITEMARRAY;         PROCEDURE EXPAND(N); INTEGER N;        BEGIN            INTEGER I;            REF(ITEMARRAY) TEMP;            TEMP :- NEW ITEMARRAY(N);            FOR I := 0 STEP 1 UNTIL SIZE-1 DO                TEMP.DATA(I) :- ITEMS.DATA(I);            ITEMS :- TEMP;        END EXPAND;         PROCEDURE APPEND(RI); REF(ITEM) RI;        BEGIN            IF SIZE + 1 > CAPACITY THEN            BEGIN                CAPACITY := 2 * CAPACITY;                EXPAND(CAPACITY);            END;            ITEMS.DATA(SIZE) :- RI;            SIZE := SIZE + 1;        END APPEND;         PROCEDURE APPENDALL(IL); REF(ITEMLIST) IL;        BEGIN            INTEGER I;            FOR I := 0 STEP 1 UNTIL IL.SIZE-1 DO                APPEND(IL.ELEMENT(I));        END APPENDALL;         REF(ITEM) PROCEDURE ELEMENT(I); INTEGER I;        BEGIN            IF I < 0 OR I > SIZE-1 THEN ERROR("ELEMENT: INDEX OUT OF BOUNDS");            ELEMENT :- ITEMS.DATA(I);        END ELEMENT;         REF(ITEM) PROCEDURE SETELEMENT(I, IT); INTEGER I; REF(ITEM) IT;        BEGIN            IF I < 0 OR I > SIZE-1 THEN ERROR("SETELEMENT: INDEX OUT OF BOUNDS");            ITEMS.DATA(I) :- IT;        END SETELEMENT;         REF(ITEM) PROCEDURE POP;        BEGIN            REF(ITEM) RESULT;            IF SIZE=0 THEN ERROR("POP: EMPTY ITEMLIST");            RESULT :- ITEMS.DATA(SIZE-1);            ITEMS.DATA(SIZE-1) :- NONE;            SIZE := SIZE-1;            POP :- RESULT;        END POP;         PROCEDURE SORT(COMPARE_PROC);            PROCEDURE COMPARE_PROC IS                INTEGER PROCEDURE COMPARE_PROC(IT1,IT2); REF(ITEM) IT1,IT2;;        BEGIN            PROCEDURE SWAP(I,J); INTEGER I,J;            BEGIN               REF(ITEM) T;               T :- ITEMS.DATA(I);               ITEMS.DATA(I) :- ITEMS.DATA(J);               ITEMS.DATA(J) :- T;            END SWAP;            PROCEDURE QUICKSORT(L,R); INTEGER L,R;            BEGIN               REF(ITEM) PIVOT;               INTEGER I, J;               PIVOT :- ITEMS.DATA((L+R)//2); I := L; J := R;               WHILE I <= J DO               BEGIN                  WHILE COMPARE_PROC(ITEMS.DATA(I), PIVOT) < 0 DO I := I+1;                  WHILE COMPARE_PROC(PIVOT, ITEMS.DATA(J)) < 0 DO J := J-1;                  IF I <= J THEN                  BEGIN SWAP(I,J); I := I+1; J := J-1;                  END;               END;               IF L < J THEN QUICKSORT(L, J);               IF I < R THEN QUICKSORT(I, R);            END QUICKSORT;            IF SIZE >= 2 THEN               QUICKSORT(0,SIZE-1);        END SORT;         INTEGER CAPACITY;        INTEGER SIZE;        REF(ITEMARRAY) ITEMS;         CAPACITY := 20;        SIZE := 0;        EXPAND(CAPACITY);    END ITEMLIST;      COMMENT PROBLEM SPECIFIC PART ;      ITEM CLASS REALITEM(X); LONG REAL X;    BEGIN    END REALITEM;     ITEMLIST CLASS LIST_OF_REAL;    BEGIN        LONG REAL PROCEDURE ELEMENT(I); INTEGER I;            ELEMENT := ITEMS.DATA(I) QUA REALITEM.X;         PROCEDURE APPEND(X); LONG REAL X;            THIS ITEMLIST.APPEND(NEW REALITEM(X));         PROCEDURE SORT;        BEGIN            INTEGER PROCEDURE CMP(IT1,IT2); REF(ITEM) IT1,IT2;                CMP := IF IT1 QUA REALITEM.X < IT2 QUA REALITEM.X THEN -1 ELSE                       IF IT1 QUA REALITEM.X > IT2 QUA REALITEM.X THEN +1 ELSE 0;            THIS ITEMLIST.SORT(CMP);        END SORT;         PROCEDURE OUTLIST;        BEGIN            INTEGER I;            TEXT FMT;            OUTTEXT("[");            FMT :- BLANKS(20);            FOR I := 0 STEP 1 UNTIL SIZE-1 DO            BEGIN                IF I < 3 OR I > SIZE-1-3 THEN BEGIN                    IF I > 0 THEN OUTTEXT(", ");                    FMT.PUTFIX(ELEMENT(I), 0);                    FMT.SETPOS(1);                    WHILE FMT.MORE DO                    BEGIN                        CHARACTER C;                        C := FMT.GETCHAR;                        IF C <> ' ' THEN OUTCHAR(C);                    END                END ELSE BEGIN OUTTEXT(", ..."); I := SIZE-1-3; END;            END;            OUTTEXT("]");        END OUTLIST;    END LIST_OF_REAL;      ITEM CLASS REALLISTITEM(LRL); REF(LIST_OF_REAL) LRL;    BEGIN    END REALLISTITEM;     ITEMLIST CLASS LIST_OF_REALLIST;    BEGIN        REF(LIST_OF_REAL) PROCEDURE ELEMENT(I); INTEGER I;            ELEMENT :- ITEMS.DATA(I) QUA REALLISTITEM.LRL;         PROCEDURE APPEND(LRL); REF(LIST_OF_REAL) LRL;            THIS ITEMLIST.APPEND(NEW REALLISTITEM(LRL));         PROCEDURE OUTLIST;        BEGIN            INTEGER I;            OUTTEXT("[");            FOR I := 0 STEP 1 UNTIL SIZE-1 DO            BEGIN                IF I > 0 THEN OUTTEXT(", ");                ELEMENT(I).OUTLIST;            END;            OUTTEXT("]");        END OUTLIST;    END LIST_OF_REALLIST;     REF(LIST_OF_REAL) PROCEDURE GET_PRIMES(MAX);        INTEGER MAX;    BEGIN        REF(LIST_OF_REAL) LPRIMES;        LPRIMES :- NEW LIST_OF_REAL;        IF MAX < 2 THEN            GOTO RETURN        ELSE        BEGIN            INTEGER X;            LPRIMES.APPEND(2);            FOR X := 3 STEP 2 UNTIL MAX DO BEGIN                INTEGER I;                LONG REAL P;                FOR I := 0 STEP 1 UNTIL LPRIMES.SIZE-1 DO BEGIN                    P := LPRIMES.ELEMENT(I);                    IF (X / P) = ENTIER(X / P) THEN GOTO BREAK;                END;                LPRIMES.APPEND(X);            BREAK:            END;        END;    RETURN:        GET_PRIMES :- LPRIMES;    END GET_PRIMES;     INTEGER MAXSUM, I, S, PRI, TOTAL, DI;    REF(LIST_OF_REALLIST) DESCENDANTS, ANCESTORS;    REF(LIST_OF_REAL) PRIMES, LR, LRS;    LONG REAL P, D, PR;    BOOLEAN TAKEWHILE;    MAXSUM := 99;     DESCENDANTS :- NEW LIST_OF_REALLIST;    ANCESTORS   :- NEW LIST_OF_REALLIST;    FOR I := 0 STEP 1 UNTIL MAXSUM DO BEGIN        DESCENDANTS.APPEND(NEW LIST_OF_REAL);        ANCESTORS  .APPEND(NEW LIST_OF_REAL);    END;     PRIMES :- GET_PRIMES(MAXSUM);     FOR I := 0 STEP 1 UNTIL PRIMES.SIZE-1 DO    BEGIN        P := PRIMES.ELEMENT(I);        DESCENDANTS.ELEMENT(P).APPEND(P);        FOR S := 1 STEP 1 UNTIL DESCENDANTS.SIZE-P-1 DO        BEGIN            LRS :- DESCENDANTS.ELEMENT(S);            FOR PRI := 0 STEP 1 UNTIL LRS.SIZE-1 DO            BEGIN                PR := LRS.ELEMENT(PRI);                DESCENDANTS.ELEMENT(S + P).APPEND(P * PR);            END;        END;    END;     FOR I := 0 STEP 1 UNTIL PRIMES.SIZE-1 DO    BEGIN        P := PRIMES.ELEMENT(I);        DESCENDANTS.ELEMENT(P).POP;    END;    DESCENDANTS.ELEMENT(4).POP;     TOTAL := 0;    FOR S := 1 STEP 1 UNTIL MAXSUM DO    BEGIN        LRS :- DESCENDANTS.ELEMENT(S);        LRS.SORT;        FOR DI := 0 STEP 1 UNTIL LRS.SIZE-1 DO        BEGIN            D := LRS.ELEMENT(DI);            IF D <= MAXSUM THEN            BEGIN                REF(LIST_OF_REAL) ANCD;                ANCD :- NEW LIST_OF_REAL;                ANCD.APPENDALL(ANCESTORS.ELEMENT(S));                ANCD.APPEND(S);                ANCESTORS.SETELEMENT(D, NEW REALLISTITEM(ANCD));            END            ELSE GOTO BREAK;        END;        BREAK:         OUTTEXT("[");        OUTINT(S, 0);        OUTTEXT("] LEVEL: ");        OUTINT(ANCESTORS.ELEMENT(S).SIZE, 0);        OUTIMAGE;         OUTTEXT("ANCESTORS: ");        ANCESTORS.ELEMENT(S).OUTLIST;        OUTIMAGE;         OUTTEXT("DESCENDANTS: ");        OUTINT(LRS.SIZE,0);        OUTIMAGE;         LRS.OUTLIST;        OUTIMAGE;         OUTIMAGE;        TOTAL := TOTAL + LRS.SIZE;    END;     OUTTEXT("TOTAL DESCENDANTS ");    OUTINT(TOTAL, 0);    OUTIMAGE;END.`
Output:
```[1] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 0
[]

[2] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 0
[]

[3] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 0
[]

[4] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 0
[]

[5] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 1
[6]

[6] LEVEL: 1
ANCESTORS: [5]
DESCENDANTS: 2
[8, 9]

[7] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 2
[10, 12]

[8] LEVEL: 2
ANCESTORS: [5, 6]
DESCENDANTS: 3
[15, 16, 18]

[9] LEVEL: 2
ANCESTORS: [5, 6]
DESCENDANTS: 4
[14, 20, 24, 27]

[10] LEVEL: 1
ANCESTORS: [7]
DESCENDANTS: 5
[21, 25, 30, 32, 36]

[11] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 5
[28, 40, 45, 48, 54]

[12] LEVEL: 1
ANCESTORS: [7]
DESCENDANTS: 7
[35, 42, 50, ..., 64, 72, 81]

[13] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 8
[22, 56, 63, ..., 90, 96, 108]

[14] LEVEL: 3
ANCESTORS: [5, 6, 9]
DESCENDANTS: 10
[33, 49, 70, ..., 135, 144, 162]

[15] LEVEL: 3
ANCESTORS: [5, 6, 8]
DESCENDANTS: 12
[26, 44, 105, ..., 192, 216, 243]

.....

[96] LEVEL: 1
ANCESTORS: [13]
DESCENDANTS: 31246
[623, 890, 1068, ..., 1464114717117504, 1647129056757192, 1853020188851841]

[97] LEVEL: 0
ANCESTORS: []
DESCENDANTS: 33438
[1335, 1424, 1602, ..., 2058911320946490, 2196172075676256, 2470693585135788]

[98] LEVEL: 4
ANCESTORS: [5, 6, 8, 16]
DESCENDANTS: 35772
[1246, 1501, 1780, ..., 3088366981419735, 3294258113514384, 3706040377703682]

[99] LEVEL: 1
ANCESTORS: [17]
DESCENDANTS: 38257
[194, 1869, 2225, ..., 4392344151352512, 4941387170271576, 5559060566555523]

TOTAL DESCENDANTS 546986
```

## Visual Basic .NET

It is based on the same logic as the Python script.

`Imports System.Math Module Module1    Const MAXPRIME = 99                             ' upper bound for the prime factors    Const MAXPARENT = 99                            ' greatest parent number     Const NBRCHILDREN = 547100                      ' max number of children (total descendants)     Public Primes As New Collection()               ' table of the prime factors    Public PrimesR As New Collection()              ' table of the prime factors in reversed order    Public Ancestors As New Collection()            ' table of the parent's ancestors     Public Parents(MAXPARENT + 1) As Integer        ' index table of the root descendant (per parent)    Public CptDescendants(MAXPARENT + 1) As Integer ' counter table of the descendants (per parent)    Public Children(NBRCHILDREN) As ChildStruct     ' table of the whole descendants    Public iChildren As Integer                     ' max index of the Children table     Public Delimiter As String = ", "    Public Structure ChildStruct        Public Child As Long        Public pLower As Integer        Public pHigher As Integer    End Structure    Sub Main()        Dim Parent As Short        Dim Sum As Short        Dim i As Short        Dim TotDesc As Integer = 0        Dim MidPrime As Integer         If GetPrimes(Primes, MAXPRIME) = vbFalse Then            Return        End If         For i = Primes.Count To 1 Step -1            PrimesR.Add(Primes.Item(i))        Next         MidPrime = PrimesR.Item(1) / 2         For Each Prime In PrimesR            Parents(Prime) = InsertChild(Parents(Prime), Prime)            CptDescendants(Prime) += 1             If Prime > MidPrime Then                Continue For            End If             For Parent = 1 To MAXPARENT                Sum = Parent + Prime                 If Sum > MAXPARENT Then                    Exit For                End If                 If Parents(Parent) Then                    InsertPreorder(Parents(Parent), Sum, Prime)                    CptDescendants(Sum) += CptDescendants(Parent)                End If            Next        Next         RemoveFalseChildren()         If MAXPARENT > MAXPRIME Then            If GetPrimes(Primes, MAXPARENT) = vbFalse Then                Return            End If        End If         FileOpen(1, "Ancestors.txt", OpenMode.Output)         For Parent = 1 To MAXPARENT            GetAncestors(Parent)            PrintLine(1, "[" & Parent.ToString & "] Level: " & Ancestors.Count.ToString)             If Ancestors.Count Then                Print(1, "Ancestors: " & Ancestors.Item(1).ToString)                For i = 2 To Ancestors.Count                    Print(1, ", " & Ancestors.Item(i).ToString)                Next                PrintLine(1)                Ancestors.Clear()            Else                PrintLine(1, "Ancestors: None")            End If             If CptDescendants(Parent) Then                PrintLine(1, "Descendants: " & CptDescendants(Parent).ToString)                Delimiter = ""                PrintDescendants(Parents(Parent))                PrintLine(1)                TotDesc += CptDescendants(Parent)            Else                PrintLine(1, "Descendants: None")            End If             PrintLine(1)        Next        Primes.Clear()        PrimesR.Clear()        PrintLine(1, "Total descendants " & TotDesc.ToString)        PrintLine(1)        FileClose(1)    End Sub    Function InsertPreorder(_index As Integer, _sum As Short, _prime As Short)        Parents(_sum) = InsertChild(Parents(_sum), Children(_index).Child * _prime)         If Children(_index).pLower Then            InsertPreorder(Children(_index).pLower, _sum, _prime)        End If         If Children(_index).pHigher Then            InsertPreorder(Children(_index).pHigher, _sum, _prime)        End If         Return Nothing    End Function    Function InsertChild(_index As Integer, _child As Long) As Integer        If _index Then            If _child <= Children(_index).Child Then                Children(_index).pLower = InsertChild(Children(_index).pLower, _child)            Else                Children(_index).pHigher = InsertChild(Children(_index).pHigher, _child)            End If        Else            iChildren += 1            _index = iChildren            Children(_index).Child = _child            Children(_index).pLower = 0            Children(_index).pHigher = 0        End If         Return _index    End Function    Function RemoveFalseChildren()        Dim Exclusions As New Collection         Exclusions.Add(4)        For Each Prime In Primes            Exclusions.Add(Prime)        Next         For Each ex In Exclusions            Parents(ex) = Children(Parents(ex)).pHigher            CptDescendants(ex) -= 1        Next         Exclusions.Clear()        Return Nothing    End Function    Function GetAncestors(_child As Short)        Dim Child As Short = _child        Dim Parent As Short = 0         For Each Prime In Primes            If Child = 1 Then                Exit For            End If            While Child Mod Prime = 0                Child /= Prime                Parent += Prime            End While        Next         If Parent = _child Or _child = 1 Then            Return Nothing        End If         GetAncestors(Parent)        Ancestors.Add(Parent)        Return Nothing    End Function    Function PrintDescendants(_index As Integer)        If Children(_index).pLower Then            PrintDescendants(Children(_index).pLower)        End If         Print(1, Delimiter.ToString & Children(_index).Child.ToString)        Delimiter = ", "         If Children(_index).pHigher Then            PrintDescendants(Children(_index).pHigher)        End If         Return Nothing    End Function    Function GetPrimes(ByRef _primes As Object, Optional _maxPrime As Integer = 2) As Boolean        Dim Value As Integer = 3        Dim Max As Integer        Dim Prime As Integer         If _maxPrime < 2 Then            Return vbFalse        End If         _primes.Add(2)         While Value <= _maxPrime            Max = Floor(Sqrt(Value))             For Each Prime In _primes                If Prime > Max Then                    _primes.Add(Value)                    Exit For                End If                 If Value Mod Prime = 0 Then                    Exit For                End If            Next             Value += 2        End While         Return vbTrue    End FunctionEnd Module`

## zkl

Translation of: Python
Translation of: Racket
`const maxsum=99; primes:=Utils.Generator(Import("sieve.zkl").postponed_sieve)        .pump(List,'wrap(p){ (p<=maxsum) and p or Void.Stop }); descendants,ancestors:=List()*(maxsum + 1), List()*(maxsum + 1); foreach p in (primes){   descendants[p].insert(0,p);   foreach s in ([1..descendants.len() - p - 1]){      descendants[s + p].merge(descendants[s].apply('*(p)));   }}     // descendants[prime] is a list that starts with prime, remove prime. 4: ???foreach p in (primes + 4) { descendants[p].pop(0) } ta,td:=0,0;foreach s in ([1..maxsum]){   foreach d in (descendants[s].filter('<=(maxsum))){      ancestors[d]=ancestors[s].copy() + s;   }    println("%2d Ancestors: ".fmt(s),ancestors[s].len() and ancestors[s] or "None");   println("   Descendants: ", if(z:=descendants[s]) 				String(z.len()," : ",z) else "None");   ta+=ancestors[s].len(); td+=descendants[s].len();} println("Total ancestors: %,d".fmt(ta));println("Total descendants: %,d".fmt(td));`
Output:
``` 1 Ancestors: None
Descendants: None
2 Ancestors: None
Descendants: None
3 Ancestors: None
Descendants: None
4 Ancestors: None
Descendants: None
5 Ancestors: None
Descendants: 1 : L(6)
6 Ancestors: L(5)
Descendants: 2 : L(8,9)
7 Ancestors: None
Descendants: 2 : L(10,12)
8 Ancestors: L(5,6)
Descendants: 3 : L(15,16,18)
9 Ancestors: L(5,6)
Descendants: 4 : L(14,20,24,27)
10 Ancestors: L(7)
Descendants: 5 : L(21,25,30,32,36)
11 Ancestors: None
Descendants: 5 : L(28,40,45,48,54)
12 Ancestors: L(7)
Descendants: 7 : L(35,42,50,60,64,72,81)
13 Ancestors: None
Descendants: 8 : L(22,56,63,75,80,90,96,108)
14 Ancestors: L(5,6,9)
Descendants: 10 : L(33,49,70,84,100,120,128,135,144,162)
15 Ancestors: L(5,6,8)
Descendants: 12 : L(26,44,105,112,125,126,150,160,180,192,216,243)

18 Ancestors: L(5,6,8)
Descendants: 19 : L(65,77,78,110,132,196,280,315,336,375,378,400,450,480,512,540,576,648,729)
46 Ancestors: L(7,10,25)
Descendants: 557 : L(129,205,246,493,518,529,740,806,888,999,1364,1508,1748,2552,2871,3128,3255,3472,3519,3875,...)
99 Ancestors: L(17)
Descendants: 38257 : L(194,1869,2225,2670,2848,3204,3237,4029,4565,5037,5478,5829,6549,6837,7189,8134,8165,9709,9798,10270,...)
Total ancestors: 179
Total descendants: 546,986
```