A175069 a(n) = product of perfect divisors of n / n.

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10

Offset: 1

Author

Jaroslav Krizek, Jan 23 2010

Keywords

• nonn

Comments

A perfect divisor of n is a divisor d such that d^k = n for some k >= 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A175068.

Programs

Mathematica

Table[Apply[Times, Select[Divisors@ n, Or[# == 1, #^IntegerExponent[n, #] == n] &]]/n, {n, 105}] (* Michael De Vlieger, Nov 21 2017 *)

PARI

A175068(n) = { my(m=1); fordiv(n,d,if((1==d)||(d^valuation(n,d))==n,m*=d)); (m); };
A175069(n) = (A175068(n)/n); \\ Antti Karttunen, Nov 21 2017

Formula

a(n) = A175068(n) / n. a(n) > 1 for perfect powers n = A001597(m) for m > 2.