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A339638
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Number of nonempty sets of distinct positive integers that have a least common multiple <= n.
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1
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1, 3, 5, 9, 11, 21, 23, 31, 35, 45, 47, 91, 93, 103, 113, 129, 131, 175, 177, 221, 231, 241, 243, 427, 431, 441, 449, 493, 495, 713, 715, 747, 757, 767, 777, 1177, 1179, 1189, 1199, 1383, 1385, 1603, 1605, 1649, 1693, 1703, 1705, 2457, 2461, 2505, 2515, 2559, 2561, 2745, 2755
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} Sum_{d|k} mu(k/d) * (2^tau(d) - 1), where tau = A000005.
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EXAMPLE
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a(5) = 11 sets: {1}, {2}, {3}, {4}, {5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 4} and {1, 2, 4}.
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MATHEMATICA
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Table[Sum[Sum[MoebiusMu[k/d] (2^DivisorSigma[0, d] - 1), {d, Divisors[k]}], {k, n}], {n, 55}]
Accumulate[Table[Sum[MoebiusMu[k/d] (2^DivisorSigma[0, d] - 1), {d, Divisors[k]}], {k, 1, 60}]] (* Vaclav Kotesovec, Dec 25 2020 *)
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PROG
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(PARI) a(n) = sum(k=1, n, sumdiv(k, d, moebius(k/d) * (2^numdiv(d) - 1))); \\ Michel Marcus, Dec 11 2020
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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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