[seqfan] Re: Integers with a peculiar divisibility property

[Harvey P. Dale]

        Adopting Sean's understanding of the definition, here are the terms up to 100,000: 1, 2, 4, 8, 16, 19, 38, 76, 152, 304, 608, 1216, 1824, 3744, 3840, 4864, 6400, 7904, 11520, 14592, 19200, 21888, 23712, 24320, 25536, 32768, 33696, 34560, 43776, 71136, 72960, 80640.
        Best,
        Harvey


-----Original Message-----
From: SeqFan <seqfan-bounces at list.seqfan.eu> On Behalf Of Sean A. Irvine
Sent: Sunday, January 6, 2019 10:40 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Integers with a peculiar divisibility property

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<mailto: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?
>
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