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A336590
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Numbers k such that k/A008834(k) is squarefree, where A008834(k) is the largest cube dividing k.
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5
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1, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88
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OFFSET
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1,2
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COMMENTS
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Numbers such that none of the exponents in their prime factorization is of the form 3*m + 2.
Cohen (1962) proved that for a given number k >= 2 the asymptotic density of numbers whose exponents in their prime factorization are of the forms k*m or k*m + 1 only is zeta(k)/zeta(2). In this sequence k = 3, and therefore its asymptotic density is zeta(3)/zeta(2) = 6*zeta(3)/Pi^2 = 0.7307629694... (A253905).
Also, numbers k whose number of divisors, A000005(k), is not divisible by 3, i.e., complement of A059269.
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LINKS
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EXAMPLE
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6 is a term since 6 = 2^1 * 3^1 and 1 is not of the form 3*m + 2.
9 is not a term since 9 = 3^2 and 2 is of the form 3*m + 2.
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MATHEMATICA
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Select[Range[100], Max[Mod[FactorInteger[#][[;; , 2]], 3]] < 2 &]
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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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