A286530 a(n) = d(n+d(n)) - d(n), where d(n) is the number of divisors of n (A000005).

1, 1, 0, -1, 0, 0, 1, 2, 3, 0, 0, 0, 2, 2, -2, -1, 0, 2, 2, -2, -1, 0, 1, -2, 3, 4, -2, -2, 0, -4, 2, -2, -2, 0, 0, -3, 2, 4, -2, 2, 0, -2, 4, 0, -2, 2, 1, -6, 3, 2, 0, -2, 2, -4, -2, -1, -2, 0, 0, 0, 4, 4, -2, -5, 0, -4, 2, -2, -2, 0, 0, 0, 4, 4, -1, -2, 1, -4, 3, 2, -1, 0, 2, 0, -2, 8, 0, 4, 2, -4, 0, 0, -2, 2, 2, 0, 4, 2, 2, -7, 0, 0, 6, 2, -6, 4, 0, 4, 2

Offset: 1

Author

Antti Karttunen, May 21 2017

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A286529, A286480.

Cf. A175304 (the positions of zeros).

Programs

Mathematica

Table[DivisorSigma[0, n + DivisorSigma[0, n]] - DivisorSigma[0, n], {n, 109}] (* Michael De Vlieger, May 21 2017 *)

PARI

A286530(n) = (numdiv(n+numdiv(n)) - numdiv(n));

Python

from sympy import divisor_count as d
def a(n): return d(n + d(n)) - d(n) # Indranil Ghosh, May 21 2017

Scheme

(define (A286530 n) (- (A286529 n) (A000005 n)))

Formula

a(n) = A286529(n) - A000005(n) = A000005(n+A000005(n)) - A000005(n).