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A296302
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Number of aperiodic compositions of n with relatively prime parts. Number of compositions of n with relatively prime parts and relatively prime run-lengths.
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25
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1, 0, 2, 5, 14, 24, 62, 114, 249, 480, 1022, 1978, 4094, 8064, 16348, 32520, 65534, 130512, 262142, 523270, 1048444, 2095104, 4194302, 8384316, 16777185, 33546240, 67108356, 134201398, 268435454, 536837136, 1073741822, 2147418240, 4294965244, 8589803520
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OFFSET
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1,3
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LINKS
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FORMULA
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a = mu * mu * c, where * is Dirichlet convolution and c(n) = 2^(n-1).
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EXAMPLE
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The a(6) = 24 aperiodic compositions with relatively prime parts are:
(15), (51),
(114), (123), (132), (141), (213), (231), (312), (321), (411),
(1113), (1122), (1131), (1221), (1311), (2112), (2211), (3111),
(11112), (11121), (11211), (12111), (21111).
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MATHEMATICA
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Table[DivisorSum[n, Function[d, MoebiusMu[n/d]*DivisorSum[d, MoebiusMu[#]*2^(d/#-1)&]]], {n, 20}]
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CROSSREFS
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Cf. A000005, A000740, A000837, A007427, A008683, A008965, A059966, A060223, A100953, A228369, A281013.
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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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