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A067259
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Cube-free numbers which are not squarefree.
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11
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)=m iff A051903(m)=2.
Let us introduce a function D(n)=sigma_0(n)/(2^(alfa(1)+...+alfa(r)), sigma_0(n) number of divisors of n (A000005), prime factorization of n=p(1)^alfa(1) * ... * p(r)^alfa(r), alfa(1)+...+alfa(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. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Sep 21 2008]
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LINKS
| Eric Weisstein's World of Mathematics, Cube-free
Eric Weisstein's World of Mathematics, Squarefree
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MATHEMATICA
| f[n_]:=Union[Last/@FactorInteger[n]][[ -1]]; lst={}; Do[If[f[n]==2, AppendTo[lst, n]], {n, 2, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 12 2010]
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CROSSREFS
| Cf. A004709, A005117.
Sequence in context: A059269 A081619 A038109 * A060687 A181023 A084789
Adjacent sequences: A067256 A067257 A067258 * A067260 A067261 A067262
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 20 2002
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