A173439 Number of divisors d of number n such that sigma(d) divides sigma(n).

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

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Cf. A000005, A000203, A173440.

Sequence in context: A048003 A098219 A368883 * A322483 A061389 A366763

Adjacent sequences: A173436 A173437 A173438 * A173440 A173441 A173442

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