A304327 Number of ways to write n as a product of a perfect power and a squarefree number.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Author

Gus Wiseman, May 10 2018

Keywords

• nonn

Comments

First term greater than 2 is a(746496) = 3.

Examples

			The a(746496) = 3 ways are 12^5*3, 72^3*2, 864^2*1.
		

Links

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

Crossrefs

Cf. A000961, A001055, A001597, A005117, A007916, A034444, A091050, A183096, A203025, A246549, A303386, A304326, A304328.

Programs

Mathematica

Table[Length[Select[Divisors[n],(#===1||GCD@@FactorInteger[#][[All,2]]>1)&&SquareFreeQ[n/#]&]],{n,100}]

PARI

A304327(n) = sumdiv(n,d,issquarefree(n/d)*((1==d)||ispower(d))); \\ Antti Karttunen, Jul 29 2018

Extensions

More terms from Antti Karttunen, Jul 29 2018