A327529 Maximum divisor of n that is 1 or whose prime indices are relatively prime.

1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 14, 15, 16, 1, 18, 1, 20, 1, 22, 1, 24, 1, 26, 1, 28, 1, 30, 1, 32, 33, 34, 35, 36, 1, 38, 1, 40, 1, 42, 1, 44, 45, 46, 1, 48, 1, 50, 51, 52, 1, 54, 55, 56, 1, 58, 1, 60, 1, 62, 1, 64, 1, 66, 1, 68, 69, 70, 1, 72, 1, 74

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 number of divisors of n that are 1 or whose prime indices are relatively prime is A327530(n).

Links

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

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Formula

a(n) = n if n is in A289509, otherwise a(n) = 1.

Maple

g:= proc(n)  uses numtheory; igcd(op(map(pi, factorset(n))))=1 end proc:
seq(`if`(g(n), n, 1), n=1..100); # Robert Israel, Sep 19 2019

Mathematica

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

Crossrefs

See link for additional cross-references.

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

Sequence in context: A009531 A124625 A327512 * A318775 A317500 A339420

Adjacent sequences: A327526 A327527 A327528 * A327530 A327531 A327532

Keyword

nonn

Author

Gus Wiseman, Sep 17 2019

Status

approved