login
Values of sigma_0(n) for n in A162279.
2

%I #4 Mar 30 2012 17:35:23

%S 4,4,4,4,4,8,4,8,4,4,4,4,8,4,8,4,4,8,4,4,8,12,4,8,4,8,4,4,4,8,6,4,4,8,

%T 4,8,12,4,4,4,8,4,4,4,4,8,4,8,12,4,4,8,16,4,8,12,4,8,4,6,4,4,12,4,8,4,

%U 4,8,4,12,4,8,4,8,12,4,4,8,6,4,8,16,12,4,4,4,4,8,4,12,4,8,4,4,8,4,8,12,4,8

%N Values of sigma_0(n) for n in A162279.

%C No primes can appear in this sequence; to have sigma_0(n) = p, a prime, we must have n = q^{p-1} for some prime q, and each such n for fixed p will have a distinct value for sigma(n).

%C Conjecture: every composite number appears in this sequence. - _Max Alekseyev_

%C Up to sigma(n) = 500000, the only odd value is 9, for 106276 = 326^2 and 165649 = 407^2; these have sigma(n) = 187131.

%H Franklin T. Adams-Watters, <a href="/A162279/a162279.txt">Table of duplicate sigma values up to sigma(n) = 10000</a>

%F a(n) = A000005(A162279(n)) = A000005(A162280(n)).

%Y Cf. A000005, A162279.

%K nonn

%O 1,1

%A _Franklin T. Adams-Watters_, Jun 29 2009