# [seqfan] Re: A striking coincidence: A006863 vs. A143407

Joerg Arndt arndt at jjj.de
Sun Mar 20 09:43:53 CET 2016

```The Staudt-Clausen Theorem sort-of-ish explains it:
http://mathworld.wolfram.com/vonStaudt-ClausenTheorem.html

Open problem:
an algorithm for isA002322().
We do have (Pari/GP) istotient() (==isA000010()),
Max Alexeyev might have had a hand in it.

Best regards,   jj

P.S.: questions arose with https://oeis.org/draft/A270562

* Joerg Arndt <arndt at jjj.de> [Mar 20. 2016 07:52]:
>  https://oeis.org/A006863  Denominator of B_{2n}/(-4n), where B_m are the Bernoulli numbers.
>  https://oeis.org/A143407  Largest number k such that the reduced totient function psi(k) = A002174(n).
>
> Looong lines needed:
> A006863: 1, 24, 240, 504, 480, 264, 65520, 24, 16320, 28728, 13200, 552, 131040, 24, 6960, 171864, 32640, 24, 138181680, 24, 1082400, 151704, 5520, 1128, 4455360, 264, 12720, ...
> A143407: 2, 24, 240, 504, 480, 264, 65520,     16320, 28728, 13200, 552, 131040,     6960, 171864, 32640,     138181680,     1082400, 151704, 5520, 1128, 4455360,      12720, ...
>
> In A143407 there is the formula A143407(n) = A006863(A002174(n)/2) for n>1.
> Is there any theorem/reference for this?
>
> Best regards,   jj
>
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```