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

1,4

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A132747 A301979 A183063 * A172441 A359495 A053399

Adjacent sequences: A318976 A318977 A318978 * A318980 A318981 A318982

Keyword

nonn

Author

Gus Wiseman, Sep 06 2018

Status

approved