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A097377
a(n) = CubeFreeKernel(n) + 1.
2
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
1,1
LINKS
Eric Weisstein's World of Mathematics, Cubefree.
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
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 *)
PROG
(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
CROSSREFS
Sequence in context: A245350 A307282 A245354 * A234741 A063917 A234344
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 11 2004
STATUS
approved