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%I #11 Feb 01 2024 08:30:25
%S 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,
%T 10,29,30,31,32,5,34,35,36,37,38,39,40,21,42,43,44,45,46,47,48,13,50,
%U 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
%N a(n) = CubeFreeKernel(n) + 1.
%H Amiram Eldar, <a href="/A097377/b097377.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cubefree.html">Cubefree</a>.
%F a(n) = A007948(n) + 1.
%F 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
%t 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 *)
%o (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
%Y Cf. A097380, A004709.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 11 2004
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