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A304327 Number of ways to write n as a product of a perfect power and a squarefree number. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A198293 A043281 A320267 * A307428 A061704 A325837

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

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Last modified November 15 11:14 EST 2019. Contains 329144 sequences. (Running on oeis4.)