[seqfan] Re: Integers with a peculiar divisibility property
Sean A. Irvine
sairvin at gmail.com
Mon Jan 7 04:39:30 CET 2019
Hi Allan,
I'm not seeing some of the values you report, for example, I get
sigma(sigma(21^4))/21^2 = 17746/21.
Did you mean divisible by n rather than n^2?
For sigma(sigma(n^4)) divisible by n^2, I get
1, 2, 4, 8, 16, 19, 38, 76, 152, 304, 608, 1216, 1824, 3744, 3840, 4864,
6400, ...
(still not in the OEIS though)
Sean.
On Mon, 7 Jan 2019 at 14:02, Allan Wechsler <acwacw at gmail.com> wrote:
> Let sigma be the familiar sum-of-divisors function.
>
> While hunting multiply perfect numbers, I learned that
>
> sigma(19^4) = 151 * 911,
>
> and sigma(151) and sigma(911) are both divisible by 19. This prompted me to
> investigate which numbers n have sigma(sigma(n^4)) divisible by n^2.
>
> I wrote a Haskell one-liner to list them -- but it computes sigma by brute
> force, so it's very very slow. So far it has found:
>
> 1,2,4,8,16,19,21,25,32,38,42,50,57,64 ... which is not in OEIS.
>
> The "primitive" elements (not products of smaller elements) are 2, 19, 25,
> ... and even this tiny three-element sequence is not in OEIS. Can anyone
> whip up a faster program to look for bigger primitives?
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
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