

A318979


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


0



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
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OFFSET

1,4


COMMENTS

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


LINKS

Table of n, a(n) for n=1..87.


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.
Sequence in context: A132747 A301979 A183063 * A172441 A053399 A322996
Adjacent sequences: A318976 A318977 A318978 * A318980 A318981 A318982


KEYWORD

nonn


AUTHOR

Gus Wiseman, Sep 06 2018


STATUS

approved



