A173440 Number of divisors d of number n such that sigma(d) does not divide sigma(n).

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 3, 0, 2, 0, 1, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 6, 1, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 5, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 0, 5, 3, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 1, 0, 0, 0, 4, 0, 2, 1, 5, 0, 0, 0, 1, 0

Offset

1,12

Comments

a(n) = A000005(n) - A173439(n).

a(n) = 0 for squarefree numbers (A005117).

Links

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

Example

For n = 12: a(12) = 2; sigma(12) = 28, divisors of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d):1, 3, 4, 7, 12, 28; sigma(d) does not divide sigma(n) for 2 divisors d: 2 and 6.

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))); };
A173440(n) = (numdiv(n) - A173439(n)); \\ Antti Karttunen, Nov 23 2017
(Sage) A173440 = lambda n: len([d for d in divisors(n) if not sigma(d).divides(sigma(n))]) # D. S. McNeil, Dec 08 2010

Crossrefs

Cf. A000005, A000203, A005117, A173439.

Sequence in context: A321374 A262889 A083059 * A348341 A330936 A284687

Adjacent sequences: A173437 A173438 A173439 * A173441 A173442 A173443

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