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A063966
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Number of Abelian groups of order <= n.
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10
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1, 2, 3, 5, 6, 7, 8, 11, 13, 14, 15, 17, 18, 19, 20, 25, 26, 28, 29, 31, 32, 33, 34, 37, 39, 40, 43, 45, 46, 47, 48, 55, 56, 57, 58, 62, 63, 64, 65, 68, 69, 70, 71, 73, 75, 76, 77, 82, 84, 86, 87, 89, 90, 93, 94, 97, 98, 99, 100, 102, 103, 104, 106, 117, 118, 119, 120, 122
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OFFSET
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1,2
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LINKS
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FORMULA
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More accurately, a(n) = A021002 * n + A084892 * n^(1/2) + A084893 * n^(1/3) + O(n^(50/199 + eps)), where eps>0 is arbitrarily small (Liu, 1993). - Amiram Eldar, Sep 23 2023
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MAPLE
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with(combinat): readlib(ifactors): total := 0: for n from 1 to 100 do ans := 1: for i from 1 to nops(ifactors(n)[2]) do ans := ans*numbpart(ifactors(n)[2][i][2]) od: printf(`%d, `, total+ans): total := total+ans: od:
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MATHEMATICA
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Accumulate[Table[FiniteAbelianGroupCount[n], {n, 1, 200}]] (* Geoffrey Critzer, Dec 28 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Sep 04 2001
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EXTENSIONS
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STATUS
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approved
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