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Numbers whose count of divisors is prime: Difference between revisions
Numbers whose count of divisors is prime (view source)
Revision as of 18:40, 11 July 2021
, 2 years ago→{{header|Nim}}
(→{{header|Go}}: Takes account of Horsth's observation that only square numbers need to be tested.) |
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73441 76729 78961 80089 83521 85849 94249 96721 97969
</pre>
=={{header|Nim}}==
Checking only divisors of squares (see discussion).
<lang Nim>import math, sequtils, strformat, strutils
func divCount(n: Positive): int =
var n = n
for d in 1..n:
if d * d > n: break
if n mod d == 0:
inc result
if n div d != d:
inc result
func isOddPrime(n: Positive): bool =
if n < 3 or n mod 2 == 0: return false
if n mod 3 == 0: return n == 3
var d = 5
while d <= sqrt(n.toFloat).int:
if n mod d == 0: return false
inc d, 2
if n mod d == 0: return false
inc d, 4
result = true
iterator numWithOddPrimeDivisorCount(lim: Positive): int =
for k in 1..sqrt(lim.toFloat).int:
let n = k * k
if n.divCount().isOddPrime():
yield n
var list = toSeq(numWithOddPrimeDivisorCount(1000))
echo &"Found {list.len} numbers between 1 and 999 whose number of divisors is an odd prime:"
echo list.join(" ")
echo()
list = toSeq(numWithOddPrimeDivisorCount(100_000))
echo &"Found {list.len} numbers between 1 and 99_999 whose number of divisors is an odd prime:"
for i, n in list:
stdout.write &"{n:5}", if (i + 1) mod 10 == 0: '\n' else: ' '
echo()</lang>
{{out}}
<pre>Found 16 numbers between 1 and 999 whose number of divisors is an odd prime:
4 9 16 25 49 64 81 121 169 289 361 529 625 729 841 961
Found 79 numbers between 1 and 99_999 whose number of divisors is an odd prime:
4 9 16 25 49 64 81 121 169 289
361 529 625 729 841 961 1024 1369 1681 1849
2209 2401 2809 3481 3721 4096 4489 5041 5329 6241
6889 7921 9409 10201 10609 11449 11881 12769 14641 15625
16129 17161 18769 19321 22201 22801 24649 26569 27889 28561
29929 32041 32761 36481 37249 38809 39601 44521 49729 51529
52441 54289 57121 58081 59049 63001 65536 66049 69169 72361
73441 76729 78961 80089 83521 85849 94249 96721 97969</pre>
=={{header|Pascal}}==
<lang pascal>program FacOfInteger;
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