Zumkeller numbers: Difference between revisions
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First 40 odd zumkeller numbers are: [945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8415, 8505, 8925, 9135, 9555, 9765, 10395, 11655, 12285, 12705, 12915, 13545, 14175, 14805, 15015, 15435, 16065, 16695, 17325, 17955, 18585, 19215, 19305]
First 40 odd zumkeller numbers that don't end in a 5 are: [81081, 153153, 171171, 189189, 207207, 223839, 243243, 261261, 279279, 297297, 351351, 459459, 513513, 567567, 621621, 671517, 729729, 742203, 783783, 793611, 812889, 837837, 891891, 908523, 960687, 999999, 1024947, 1054053, 1072071, 1073709, 1095633, 1108107, 1145529, 1162161, 1198197, 1224531, 1270269, 1307691, 1324323, 1378377]</pre>
=={{header|Typescript}}==
{{trans|Go}}
<syntaxhighlight lang="typescript">
/**
* return an array of divisors of a number(n)
* @params {number} n The number to find divisors from
* @return {number[]} divisors of n
*/
function getDivisors(n: number): number[] {
//initialize divisors array
let divisors: number[] = [1, n]
//loop through all numbers from 2 to sqrt(n)
for (let i = 2; i*i <= n; i++) {
// if i is a divisor of n
if (n % i == 0) {
// add i to divisors array
divisors.push(i);
// quotient of n/i is also a divisor of n
let j = n/i;
// if quotient is not equal to i
if (i != j) {
// add quotient to divisors array
divisors.push(j);
}
}
}
return divisors
}
/**
* return sum of an array of number
* @param {number[]} arr The array we need to sum
* @return {number} sum of arr
*/
function getSum(arr: number[]): number {
return arr.reduce((prev, curr) => prev + curr, 0)
}
/**
* check if there is a subset of divisors which sums to a specific number
* @param {number[]} divs The array of divisors
* @param {number} sum The number to check if there's a subset of divisors which sums to it
* @return {boolean} true if there is a subset of divisors which sums to sum, false otherwise
*/
function isPartSum(divs: number[], sum: number): boolean {
// if sum is 0, the partition is sum up to the number(sum)
if (sum == 0) return true;
//get length of divisors array
let len = divs.length;
// if divisors array is empty the partion doesnt not sum up to the number(sum)
if (len == 0) return false;
//get last element of divisors array
let last = divs[len - 1];
//create a copy of divisors array without the last element
const newDivs = [...divs];
newDivs.pop();
// if last element is greater than sum
if (last > sum) {
// recursively check if there's a subset of divisors which sums to sum using the new divisors array
return isPartSum(newDivs, sum);
}
// recursively check if there's a subset of divisors which sums to sum using the new divisors array
// or if there's a subset of divisors which sums to sum - last using the new divisors array
return isPartSum(newDivs, sum) || isPartSum(newDivs, sum - last);
}
/**
* check if a number is a Zumkeller number
* @param n The number to check if it's a Zumkeller number
* @returns true if n is a Zumkeller number, false otherwise
*/
function isZumkeller(n: number): boolean {
// get divisors of n
let divs = getDivisors(n);
// get sum of divisors of n
let sum = getSum(divs);
// if sum is odd can't be split into two partitions with equal sums
if (sum % 2 == 1) return false;
// if n is odd use 'abundant odd number' optimization
if (n % 2 == 1) {
let abundance = sum - 2 * n
return abundance > 0 && abundance%2 == 0;
}
// if n and sum are both even check if there's a partition which totals sum / 2
return isPartSum(divs, sum/2);
}
/**
* find x zumkeller numbers
* @param {number} x The number of zumkeller numbers to find
* @returns {number[]} array of x zumkeller numbers
*/
function getXZumkelers(x: number): number[] {
let zumkellers: number[] = [];
let i = 2;
let count= 0;
while (count < x) {
if (isZumkeller(i)) {
zumkellers.push(i);
count++;
}
i++;
}
return zumkellers;
}
/**
* find x Odd Zumkeller numbers
* @param {number} x The number of odd zumkeller numbers to find
* @returns {number[]} array of x odd zumkeller numbers
*/
function getXOddZumkelers(x: number): number[] {
let oddZumkellers: number[] = [];
let i = 3;
let count = 0;
while (count < x) {
if (isZumkeller(i)) {
oddZumkellers.push(i);
count++;
}
i += 2;
}
return oddZumkellers;
}
/**
* find x odd zumkeller number which are not end with 5
* @param {number} x The number of odd zumkeller numbers to find
* @returns {number[]} array of x odd zumkeller numbers
*/
function getXOddZumkellersNotEndWith5(x: number): number[] {
let oddZumkellers: number[] = [];
let i = 3;
let count = 0;
while (count < x) {
if (isZumkeller(i) && i % 10 != 5) {
oddZumkellers.push(i);
count++;
}
i += 2;
}
return oddZumkellers;
}
//get the first 220 zumkeller numbers
console.log("First 220 Zumkeller numbers: ", getXZumkelers(220));
//get the first 40 odd zumkeller numbers
console.log("First 40 odd Zumkeller numbers: ", getXOddZumkelers(40));
//get the first 40 odd zumkeller numbers which are not end with 5
console.log("First 40 odd Zumkeller numbers which are not end with 5: ", getXOddZumkellersNotEndWith5(40));
</syntaxhighlight>
{{out}}
<pre>
"First 220 Zumkeller numbers: ", [6, 12, 20, 24, 28, 30, 40, 42, 48, 54, 56, 60, 66, 70, 78, 80, 84, 88, 90, 96, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 150, 156, 160, 168, 174, 176, 180, 186, 192, 198, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270, 272, 276, 280, 282, 294, 300, 304, 306, 308, 312, 318, 320, 330, 336, 340, 342, 348, 350, 352, 354, 360, 364, 366, 368, 372, 378, 380, 384, 390, 396, 402, 408, 414, 416, 420, 426, 432, 438, 440, 444, 448, 456, 460, 462, 464, 468, 474, 476, 480, 486, 490, 492, 496, 498, 500, 504, 510, 516, 520, 522, 528, 532, 534, 540, 544, 546, 550, 552, 558, 560, 564, 570, 572, 580, 582, 588, 594, 600, 606, 608, 612, 616, 618, 620, 624, 630, 636, 640, 642, 644, 650, 654, 660, 666, 672, 678, 680, 684, 690, 696, 700, 702, 704, 708, 714, 720, 726, 728, 732, 736, 740, 744, 750, 756, 760, 762, 768, 770, 780, 786, 792, 798, 804, 810, 812, 816, 820, 822, 828, 832, 834, 836, 840, 852, 858, 860, 864, 868, 870, 876, 880, 888, 894, 896, 906, 910, 912, 918, 920, 924, 928, 930, 936, 940, 942, 945, 948, 952, 960, 966, 972, 978, 980, 984]
"First 40 odd Zumkeller numbers: ", [945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8415, 8505, 8925, 9135, 9555, 9765, 10395, 11655, 12285, 12705, 12915, 13545, 14175, 14805, 15015, 15435, 16065, 16695, 17325, 17955, 18585, 19215, 19305]
"First 40 odd Zumkeller numbers which are not end with 5: ", [81081, 153153, 171171, 189189, 207207, 223839, 243243, 261261, 279279, 297297, 351351, 459459, 513513, 567567, 621621, 671517, 729729, 742203, 783783, 793611, 812889, 837837, 891891, 908523, 960687, 999999, 1024947, 1054053, 1072071, 1073709, 1095633, 1108107, 1145529, 1162161, 1198197, 1224531, 1270269, 1307691, 1324323, 1378377]
</pre>
=={{header|Visual Basic .NET}}==
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