A318979 Number of divisors of n with relatively prime prime indices, meaning they belong to A289509.

0, 1, 0, 2, 0, 2, 0, 3, 0, 2, 0, 4, 0, 2, 1, 4, 0, 3, 0, 4, 0, 2, 0, 6, 0, 2, 0, 4, 0, 5, 0, 5, 1, 2, 1, 6, 0, 2, 0, 6, 0, 4, 0, 4, 2, 2, 0, 8, 0, 3, 1, 4, 0, 4, 1, 6, 0, 2, 0, 9, 0, 2, 0, 6, 0, 5, 0, 4, 1, 5, 0, 9, 0, 2, 2, 4, 1, 4, 0, 8, 0, 2, 0, 8, 1, 2, 0

Offset: 1

Author

Gus Wiseman, Sep 06 2018

Keywords

• nonn

Comments

A prime index of n is a number m such that prime(m) divides n.

Examples

			The divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36, corresponding to the prime index multisets (), (1), (2), (11), (12), (22), (112), (122), (1122) respectively. Of these, only (1), (11), (12), (112), (122), (1122) are relatively prime, corresponding to the divisors 2, 4, 6, 12, 18, 36, so a(36) = 6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A000837, A001221, A018783, A056239, A289508, A289509, A296150, A298748, A318978, A327657.

Programs

Mathematica

Table[Length[Select[Divisors[n],GCD@@PrimePi/@FactorInteger[#][[All,1]]==1&]],{n,100}]

PARI

a(n) = sumdiv(n, d, gcd(apply(x->primepi(x), factor(d)[,1])) == 1); \\ Michel Marcus, Jan 09 2019

Formula

a(n) = A000005(n) - A327657(n). - Antti Karttunen, Dec 05 2021