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A108347
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Numbers of the form (3^i)*(5^j)*(7^k), with i, j, k >= 0.
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8
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1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 49, 63, 75, 81, 105, 125, 135, 147, 175, 189, 225, 243, 245, 315, 343, 375, 405, 441, 525, 567, 625, 675, 729, 735, 875, 945, 1029, 1125, 1215, 1225, 1323, 1575, 1701, 1715, 1875, 2025, 2187, 2205, 2401, 2625, 2835, 3087
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OFFSET
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1,2
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COMMENTS
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The Heinz numbers of the partitions into parts 2,3, and 4 (including the number 1, the Heinz number of the empty partition). We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [2,3,3,4] the Heinz number is 3*5*5*7 = 525; it is in the sequence. - Emeric Deutsch , May 21 2015
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = (3*5*7)/((3-1)*(5-1)*(7-1)) = 35/16. - Amiram Eldar, Sep 22 2020
a(n) ~ exp((6*log(3)*log(5)*log(7)*n)^(1/3)) / sqrt(105). - Vaclav Kotesovec, Sep 23 2020
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MAPLE
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with(numtheory): S := {}: for j to 3100 do if `subset`(factorset(j), {3, 5, 7}) then S := `union`(S, {j}) else end if end do: S; # Emeric Deutsch, May 21 2015
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MATHEMATICA
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With[{n = 3087}, Sort@ Flatten@ Table[3^i * 5^j * 7^k, {i, 0, Log[3, n]}, {j, 0, Log[5, n/2^i]}, {k, 0, Log[7, n/(3^i*5^j)]}]] (* Michael De Vlieger, Aug 22 2019 *)
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PROG
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(Magma) [n: n in [1..4000] | PrimeDivisors(n) subset [3, 5, 7]]; // Bruno Berselli, Sep 24 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Douglas Winston (douglas.winston(AT)srupc.com), Jul 01 2005
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STATUS
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approved
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