A327530 Number of divisors of n that are 1 or whose prime indices are relatively prime.

1, 2, 1, 3, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 2, 5, 1, 4, 1, 5, 1, 3, 1, 7, 1, 3, 1, 5, 1, 6, 1, 6, 2, 3, 2, 7, 1, 3, 1, 7, 1, 5, 1, 5, 3, 3, 1, 9, 1, 4, 2, 5, 1, 5, 2, 7, 1, 3, 1, 10, 1, 3, 1, 7, 1, 6, 1, 5, 2, 6, 1, 10, 1, 3, 3, 5, 2, 5, 1, 9, 1, 3, 1, 9, 2, 3

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers whose prime indices are relatively prime are A289509. The maximum divisor of n that is 1 or whose prime indices are relatively prime is A327529(n).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Example

The divisors of 84 that are 1 or whose prime indices are relatively prime are {1, 2, 4, 6, 12, 14, 28, 42, 84}, so a(84) = 9.

Maple

N:= 100: # for a(1)..a(N)
g:= proc(n) uses numtheory; igcd(op(map(pi, factorset(n))))=1 end proc:
V:= Vector(N, 1):
for k in select(g, [$2..N]) do
  R:=[seq(i, i=k..N, k)]:
  V[R]:= map(`+`, V[R], 1);
od:
convert(V, list); # Robert Israel, Sep 19 2019

Mathematica

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

Crossrefs

See link for additional cross-references.

Cf. A000005, A006530, A112798, A281116, A289509, A318721.

Sequence in context: A306248 A361788 A327513 * A084360 A082460 A318573

Adjacent sequences: A327527 A327528 A327529 * A327531 A327532 A327533

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved