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

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}]

Prog

(PARI) a(n) = sumdiv(n, d, !ispower(d) && !ispower(n/d)); \\ Michel Marcus, May 17 2018

Crossrefs

Cf. A000005, A001055, A007427, A007916, A034444, A045778, A162247, A183096, A281116, A301700, A303386, A303707, A304650.

Sequence in context: A344326 A007427 A048106 * A228441 A156260 A056671

Adjacent sequences: A304646 A304647 A304648 * A304650 A304651 A304652

Keyword

nonn

Author

Gus Wiseman, May 15 2018

Status

approved