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A368039
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The product of exponents of prime factorization of the nonsquarefree numbers.
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5
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2, 3, 2, 2, 4, 2, 2, 3, 2, 3, 2, 5, 4, 3, 2, 2, 4, 2, 2, 2, 3, 3, 2, 2, 6, 2, 6, 2, 2, 4, 4, 2, 3, 2, 2, 5, 2, 2, 4, 3, 6, 4, 2, 2, 3, 2, 2, 3, 2, 7, 2, 3, 3, 2, 8, 2, 2, 2, 3, 2, 2, 5, 4, 2, 3, 2, 2, 2, 2, 4, 4, 3, 2, 3, 6, 4, 2, 6, 2, 2, 4, 2, 9, 2, 5, 4, 2
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OFFSET
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1,1
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COMMENTS
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The terms of A005361 that are larger than 1, since A005361(k) = 1 if and only if k is squarefree (A005117).
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = ((zeta(2)*zeta(3)/zeta(6)) - 1/zeta(2))/(1-1/zeta(2)) = (A082695 - A059956)/A229099 = 3.406686208821... .
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MATHEMATICA
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Select[Table[Times @@ FactorInteger[n][[;; , 2]], {n, 1, 250}], # > 1 &]
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PROG
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(PARI) lista(kmax) = {my(p); for(k = 1, kmax, p = vecprod(factor(k)[, 2]); if(p > 1, print1(p, ", "))); }
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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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