A056691 Number of divisors d of n with gcd(d+1, n) = 1.

1, 1, 2, 2, 2, 1, 2, 3, 3, 2, 2, 3, 2, 2, 3, 4, 2, 2, 2, 3, 4, 2, 2, 4, 3, 2, 4, 4, 2, 3, 2, 5, 3, 2, 4, 5, 2, 2, 4, 5, 2, 1, 2, 4, 4, 2, 2, 6, 3, 3, 3, 4, 2, 3, 4, 6, 4, 2, 2, 5, 2, 2, 6, 6, 4, 3, 2, 4, 3, 3, 2, 7, 2, 2, 5, 4, 4, 2, 2, 7, 5, 2, 2, 5, 4, 2, 3, 6, 2, 5, 3, 4, 4, 2, 3, 7, 2, 3, 5, 5, 2, 3, 2, 6, 6

Offset: 1

Author

Leroy Quet, Aug 10 2000

Keywords

• nonn

Examples

			The positive divisors of 8 are 1, 2, 4 and 8. (2+1), (4+1) and (8+1) are relatively prime to 8, so a(8) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056692.

Programs

Mathematica

Table[Length[Select[Divisors[n],CoprimeQ[#+1,n]&]],{n,120}] (* Harvey P. Dale, Sep 07 2020 *)

PARI

a(n) = sumdiv(n, d, gcd(d+1, n) == 1); \\ Amiram Eldar, May 23 2025