[seqfan] Re: Sigma_2

[C Boyd]

Dear Frank,

The sequences are close, but not identical. Comparing n such that sigma_2(n) is not divisible by 5 directly with the b-file of A031363, I get that two numbers in the range 1..60755 belong only to A031363, namely 14641 (11^4) and 58564 (2^2*11^4).

In Pari:

sigma(14641,2)%5
%1 = 0
? sigma(58564,2)%5
%2 = 0

? #bnfisintnorm(bnfinit(z^2-z-1), 14641) \\ Ralf Stephan code in A031363
%3 = 5
? #bnfisintnorm(bnfinit(z^2-z-1), 58564)
%4 = 5

It looks like numbers of the form 2^(2k)*11^4 for k>=0 all share this property. There may be others, as I have not looked beyond 60755 except for numbers defined by the formula.

CB


-----Original Message-----
From: Frank Adams-Watters <franktaw at netscape.net>  Tue Mar 29 05:40:58 2016
Date: Tue, 29 Mar 2016 00:40:54 -0400
To: seqfan at list.seqfan.eu
Subject: [seqfan] Sigma_2

Is A031363 the set of all numbers n such that sigma_2(n) is not divisible by 5? If not, where is the first difference?

Franklin T. Adams-Watters