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%I #16 Nov 26 2017 07:15:19
%S 1,2,2,2,2,4,2,3,2,4,2,4,2,4,4,2,2,4,2,5,4,4,2,6,2,4,3,4,2,8,2,4,4,4,
%T 4,4,2,4,4,6,2,8,2,5,4,4,2,4,2,4,4,4,2,6,4,6,4,4,2,10,2,4,5,2,4,8,2,5,
%U 4,8,2,6,2,4,4,4,4,8,2,5,2,4,2,8,4,4,4,6,2,8,4,5,4,4,4,8,2,4,5,4,2,8,2,7,8
%N Number of divisors d of number n such that sigma(d) divides sigma(n).
%C a(n) = A000005(n) - A173440(n). a(n) = A000005(n) for squarefree numbers (A005117).
%H Antti Karttunen, <a href="/A173439/b173439.txt">Table of n, a(n) for n = 1..16384</a>
%e For n = 12, a(12) = 4; sigma(12) = 28, divisors of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d):1, 3, 4, 7, 12, 28; sigma(d) divides sigma(n) for 4 divisors d: 1, 3, 4, 12.
%t Table[DivisorSum[n, 1 &, Divisible[DivisorSigma[1, n], DivisorSigma[1, #]] &], {n, 105}] (* _Michael De Vlieger_, Nov 23 2017 *)
%o (PARI) A173439(n) = { my(s=sigma(n)); sumdiv(n,d,!(s%sigma(d))); }; \\ _Antti Karttunen_, Nov 23 2017
%o (Sage) A173439 = lambda n: len([d for d in divisors(n) if sigma(d).divides(sigma(n))]) # _D. S. McNeil_, Dec 08 2010
%Y Cf. A000005, A000203, A173440.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Feb 18 2010
%E Edited and extended by _D. S. McNeil_, Dec 08 2010
%E More terms from _Antti Karttunen_, Nov 23 2017
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