

A304326


Number of ways to write n as a product of a number that is not a perfect power and a squarefree number.


11



0, 1, 1, 1, 1, 3, 1, 0, 1, 3, 1, 3, 1, 3, 3, 0, 1, 3, 1, 3, 3, 3, 1, 2, 1, 3, 0, 3, 1, 7, 1, 0, 3, 3, 3, 3, 1, 3, 3, 2, 1, 7, 1, 3, 3, 3, 1, 2, 1, 3, 3, 3, 1, 2, 3, 2, 3, 3, 1, 7, 1, 3, 3, 0, 3, 7, 1, 3, 3, 7, 1, 3, 1, 3, 3, 3, 3, 7, 1, 2, 0, 3, 1, 7, 3, 3, 3, 2, 1
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OFFSET

1,6


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..10000


EXAMPLE

The a(180) = 7 ways are (6*30), (12*15), (18*10), (30*6), (60*3), (90*2), (180*1).


MATHEMATICA

radQ[n_]:=And[n>1, GCD@@FactorInteger[n][[All, 2]]===1];
Table[Length[Select[Divisors[n], radQ[#]&&SquareFreeQ[n/#]&]], {n, 100}]


PROG

(PARI) a(n)={sumdiv(n, d, d<>1 && !ispower(d) && issquarefree(n/d))} \\ Andrew Howroyd, Aug 26 2018


CROSSREFS

Positions of zeros are A246549. Range appears to be A075427.
Cf. A000961, A001055, A001597, A001694, A005117, A007916, A034444, A091050, A183096, A303386, A303707, A304327, A304328.
Sequence in context: A122779 A120323 A320476 * A099905 A268441 A264435
Adjacent sequences: A304323 A304324 A304325 * A304327 A304328 A304329


KEYWORD

nonn


AUTHOR

Gus Wiseman, May 10 2018


STATUS

approved



