A336387 Number of prime divisors of n that do not divide sigma(n); a(1) = 0.

0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Jul 25 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A175200 (positions of zeros).

Cf. also A173438, A336352, A336388.

Programs

Mathematica

Table[Length[Select[FactorInteger[n][[All,1]],Mod[DivisorSigma[ 1,n],#]!= 0&]],{n,110}] (* Harvey P. Dale, Jan 15 2022 *)

PARI

A336387(n) = if(1==n,0,my(s=sigma(n)); #select(p -> (s%p), factor(n)[, 1]));

Formula

a(n) = Sum_{p over distinct primes dividing n} [sigma(n) != 0 mod p].