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A304650 Number of ways to write n as a product of two positive integers, neither of which is a perfect power.

%I A304650 #7 May 17 2018 21:36:05
%S A304650 0,0,0,1,0,2,0,0,1,2,0,2,0,2,2,0,0,2,0,2,2,2,0,2,1,2,0,2,0,6,0,0,2,2,
%T A304650 2,5,0,2,2,2,0,6,0,2,2,2,0,2,1,2,2,2,0,2,2,2,2,2,0,8,0,2,2,0,2,6,0,2,
%U A304650 2,6,0,4,0,2,2,2,2,6,0,2,0,2,0,8,2,2,2,2,0,8,2,2,2,2,2,2,0,2
%N A304650 Number of ways to write n as a product of two positive integers, neither of which is a perfect power.
%e A304650 The a(60) = 8 ways to write 60 as a product of two numbers, neither of which is a perfect power, are 2*30, 3*20, 5*12, 6*10, 10*6, 12*5, 20*3, 30*2.
%t A304650 radQ[n_]:=And[n>1,GCD@@FactorInteger[n][[All,2]]===1];
%t A304650 Table[Length[Select[Divisors[n],radQ[#]&&radQ[n/#]&]],{n,100}]
%o A304650 (PARI) ispow(n) = (n==1) || ispower(n);
%o A304650 a(n) = sumdiv(n, d, !ispow(d) && !ispow(n/d)); \\ _Michel Marcus_, May 17 2018
%Y A304650 Cf. A000005, A001055, A007427, A007916, A034444, A045778, A162247, A183096, A281116, A301700, A303386, A303707, A304649.
%K A304650 nonn
%O A304650 1,6
%A A304650 _Gus Wiseman_, May 15 2018