A304650 Number of ways to write n as a product of two positive integers, neither of which is a perfect power.
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, 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, 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
Offset: 1
Keywords
Examples
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.
Crossrefs
Programs
-
Mathematica
radQ[n_]:=And[n>1,GCD@@FactorInteger[n][[All,2]]===1]; Table[Length[Select[Divisors[n],radQ[#]&&radQ[n/#]&]],{n,100}] -
PARI
ispow(n) = (n==1) || ispower(n); a(n) = sumdiv(n, d, !ispow(d) && !ispow(n/d)); \\ Michel Marcus, May 17 2018