A097377 a(n) = CubeFreeKernel(n) + 1.

2, 3, 4, 5, 6, 7, 8, 5, 10, 11, 12, 13, 14, 15, 16, 5, 18, 19, 20, 21, 22, 23, 24, 13, 26, 27, 10, 29, 30, 31, 32, 5, 34, 35, 36, 37, 38, 39, 40, 21, 42, 43, 44, 45, 46, 47, 48, 13, 50, 51, 52, 53, 54, 19, 56, 29, 58, 59, 60, 61, 62, 63, 64, 5, 66, 67, 68, 69, 70, 71, 72, 37, 74, 75

Offset: 1

Author

Reinhard Zumkeller, Aug 11 2004

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Cubefree.

Crossrefs

Cf. A097380, A004709.

Programs

Mathematica

f[p_, e_] := p^Min[e, 2]; a[1] = 2; a[n_] := 1 + Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 01 2024 *)

PARI

a(n) = {my(f = factor(n)); 1 + prod(i = 1, #f~, f[i, 1]^min(f[i, 2], 2));} \\ Amiram Eldar, Feb 01 2024

Formula

a(n) = A007948(n) + 1.

Dirichlet g.f.: zeta(s) * (1 + Product_{p prime} (1 + 1/p^(s-1) - 1/p^s + 1/p^(2*s-2) - 1/p^(2*s-1)). - Amiram Eldar, Feb 01 2024