Aliquot sequence classifications: Difference between revisions

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=={{header|Nim}}==

<syntaxhighlight lang="nim">import std/[math, strformat, times]

import ~~math~~

from std/strutils import addSep

import strformat

from strutils import addSep

import times

type

# Classification categories.

Category = enum

Category {.pure.} = enum

Unknown

Terminating = "terminating"

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# Aliquot sequence.

AliquotSeq = seq[~~int~~]

AliquotSeq = seq[int64]

const Limit = 2^47 # Limit beyond which the category is considered to be "NonTerminating".

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#---------------------------------------------------------------------------------------------------

proc sumProperDivisors(n: ~~int~~): ~~int~~ =

proc sumProperDivisors(n: int64): int64 =

## Compute the sum of proper divisors.*

if n == 1: return 0

result = 1

for d in 2..sqrt(n.~~toFloat~~).int:

for d in 2..sqrt(n.float).int:

if n mod d == 0:

inc result, d

if n div d != d:

~~inc~~ result, n div d

result += n div d

#---------------------------------------------------------------------------------------------------

iterator aliquotSeq(n: ~~int~~): ~~int~~ =

iterator aliquotSeq(n: int64): int64 =

## Yield the elements of the aliquot sequence of "n".

## Stopped if the current value is null or equal to "n".

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#---------------------------------------------------------------------------------------------------

proc classification(n: ~~int~~): tuple[cat: Category, values: AliquotSeq] =

proc classification(n: int64): tuple[cat: Category, values: AliquotSeq] =

## Return the category of the aliquot sequence of a number "n" and the sequence itself.

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for n in 1..10:

let (cat, aseq) = classification(n)

echo fmt"{n:14}: {cat:<20} {aseq}"

echo ""

for n in [11, 12, 28, 496, 220, 1184, 12496, 1264460,

for n in [int64 11, 12, 28, 496, 220, 1184, 12496, 1264460,

790, 909, 562, 1064, 1488, 15355717786080~~.int~~]:

790, 909, 562, 1064, 1488, 15355717786080]:

let (cat, aseq) = classification(n)

echo fmt"{n:14}: {cat:<20} {aseq}"