A295305 a(n) = tau(sigma(n)) - tau(n), where tau is the number of divisors (A000005) and sigma is the sum of divisors of n (A000203).

0, 0, 1, -1, 2, 2, 2, 0, -1, 2, 4, 0, 2, 4, 4, -3, 4, -2, 4, 2, 2, 5, 6, 4, -1, 4, 4, 2, 6, 4, 4, 0, 6, 4, 6, -5, 2, 8, 4, 4, 6, 4, 4, 6, 2, 8, 8, -4, 1, -2, 8, 0, 6, 8, 8, 8, 6, 8, 10, 4, 2, 8, 2, -5, 8, 7, 4, 6, 8, 7, 10, -4, 2, 4, 0, 6, 8, 8, 8, -2, -2, 8, 10, 0, 8, 8, 12, 10, 10, 0, 6, 10, 4, 11, 12, 6, 4, 0, 6, -5, 6, 8, 6, 8, 6

Offset: 1

Author

Antti Karttunen, Nov 21 2017

Keywords

• sign

Links

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

Crossrefs

Cf. A000005, A000203, A062068, A295306.

Cf. A037197 (positions of zeros), A073803 (of positive terms), A073804 (of negative terms).

Programs

Mathematica

Table[DivisorSigma[0,DivisorSigma[1,n]]-DivisorSigma[0,n],{n,110}] (* Harvey P. Dale, Oct 26 2020 *)

PARI

A295305(n) = (numdiv(sigma(n)) - numdiv(n));

Formula

a(n) = A062068(n) - A000005(n).