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A067259
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Cubefree numbers which are not squarefree.
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24
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4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, 63, 68, 75, 76, 84, 90, 92, 98, 99, 100, 116, 117, 121, 124, 126, 132, 140, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 180, 188, 196, 198, 204, 207, 212, 220, 225, 228
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OFFSET
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1,1
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COMMENTS
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Let us introduce a function D(n)=sigma_0(n)/(2^(alpha(1)+...+alpha(r)), sigma_0(n) number of divisors of n (A000005), prime factorization of n=p(1)^alpha(1) * ... * p(r)^alpha(r), alpha(1)+...+alpha(r) is sequence (A086436). This function splits the set of positive integers into subsets, according to the value of D(n). Squarefree numbers (005117) has D(n)=1, other numbers are "deviated" from the squarefree ideal and have 0 < D(n) < 1. So for D(n)=1/2 we have A048109, D(n)=3/4 we have A067295. - Ctibor O. Zizka, Sep 21 2008
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LINKS
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Eric Weisstein's World of Mathematics, Cubefree
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FORMULA
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MATHEMATICA
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Select[Range[500], Not[SquareFreeQ[#]] && FreeQ[FactorInteger[#], {_, k_ /; k>2}]&] (* Vaclav Kotesovec, Jul 09 2020 *)
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PROG
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(Haskell)
a067259 n = a067259_list !! (n-1)
a067259_list = filter ((== 2) . a051903) [1..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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