A304649 - OEIS

A304649

Number of divisors d|n such that neither d nor n/d is a perfect power greater than 1.

1, 2, 2, 1, 2, 4, 2, 0, 1, 4, 2, 4, 2, 4, 4, 0, 2, 4, 2, 4, 4, 4, 2, 4, 1, 4, 0, 4, 2, 8, 2, 0, 4, 4, 4, 5, 2, 4, 4, 4, 2, 8, 2, 4, 4, 4, 2, 4, 1, 4, 4, 4, 2, 4, 4, 4, 4, 4, 2, 10, 2, 4, 4, 0, 4, 8, 2, 4, 4, 8, 2, 6, 2, 4, 4, 4, 4, 8, 2, 4, 0, 4, 2, 10, 4, 4, 4, 4

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

EXAMPLE

The a(36) = 5 ways to write 36 as a product of two numbers that are not perfect powers greater than 1 are 2*18, 3*12, 6*6, 12*3, 18*2.

MATHEMATICA

nn=1000;

sradQ[n_]:=GCD@@FactorInteger[n][[All, 2]]===1;

Table[Length@Select[Divisors[n], sradQ[n/#]&&sradQ[#]&], {n, nn}]