A072375 Number of cubefree numbers <= n which are nonsquares having exactly one square in their factorization.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15

Offset: 1

Author

Reinhard Zumkeller, Jul 19 2002

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A072357, A072358, A060431, A271971.

Programs

Mathematica

cfnsQ[n_]:=Module[{f=FactorInteger[n][[All,2]]},Max[f]<3&&Count[f,2] == 1&&!IntegerQ[Sqrt[n]]]; Accumulate[Table[If[cfnsQ[n],1,0],{n,100}]] (* Harvey P. Dale, May 24 2017 *)

Formula

a(n) ~ c * n, where c = (6/Pi^2) * Sum_{p prime} 1/(p*(p+1)) = 0.200755... (A271971). - Amiram Eldar, Feb 16 2021