A076333 Squarefree kernels of nonsquarefree numbers.

2, 2, 3, 6, 2, 6, 10, 6, 5, 3, 14, 2, 6, 10, 22, 15, 6, 7, 10, 26, 6, 14, 30, 21, 2, 34, 6, 15, 38, 10, 3, 42, 22, 30, 46, 6, 14, 33, 10, 26, 6, 14, 58, 39, 30, 11, 62, 5, 42, 2, 66, 15, 34, 70, 6, 21, 74, 30, 38, 51, 78, 10, 6, 82, 42, 13, 57, 86, 35, 22, 30, 46, 94, 21, 6, 14, 66

Offset: 1

Author

Reinhard Zumkeller, Nov 06 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A013929.

Cf. A059956, A065463.

Programs

Mathematica

f[n_] := If[(r = Times @@ FactorInteger[n][[;; , 1]]) < n, r , 0]; Select[f /@ Range[200], # > 0 &] (* Amiram Eldar, Sep 07 2020 *)

Formula

a(n) = A007947(A013929(n)).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = (A065463 - 6/Pi^2)/(1 - 6/Pi^2)^2 = 0.627858264532... . - Amiram Eldar, Dec 09 2023