A304327 - OEIS

%I #10 Jul 30 2018 13:47:37

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A304327/b304327.txt">Table of n, a(n) for n = 1..65537</a>

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

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

%o (PARI) A304327(n) = sumdiv(n,d,issquarefree(n/d)*((1==d)||ispower(d))); \\ _Antti Karttunen_, Jul 29 2018

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

%K nonn

%O 1,8

%A _Gus Wiseman_, May 10 2018

%E More terms from _Antti Karttunen_, Jul 29 2018