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A173439
Number of divisors d of number n such that sigma(d) divides sigma(n).
2
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, 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, 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
OFFSET
1,2
COMMENTS
a(n) = A000005(n) - A173440(n). a(n) = A000005(n) for squarefree numbers (A005117).
LINKS
EXAMPLE
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.
MATHEMATICA
Table[DivisorSum[n, 1 &, Divisible[DivisorSigma[1, n], DivisorSigma[1, #]] &], {n, 105}] (* Michael De Vlieger, Nov 23 2017 *)
PROG
(PARI) A173439(n) = { my(s=sigma(n)); sumdiv(n, d, !(s%sigma(d))); }; \\ Antti Karttunen, Nov 23 2017
(Sage) A173439 = lambda n: len([d for d in divisors(n) if sigma(d).divides(sigma(n))]) # D. S. McNeil, Dec 08 2010
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 18 2010
EXTENSIONS
Edited and extended by D. S. McNeil, Dec 08 2010
More terms from Antti Karttunen, Nov 23 2017
STATUS
approved