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

1,8

Comments

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

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A043281 A365634 A320267 * A307428 A368248 A362852

Adjacent sequences: A304324 A304325 A304326 * A304328 A304329 A304330

Keyword

nonn

Author

Gus Wiseman, May 10 2018

Extensions

More terms from Antti Karttunen, Jul 29 2018

Status

approved