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A316433
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Number of integer partitions of n whose length is equal to the LCM of all parts.
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8
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1, 0, 1, 1, 1, 0, 2, 1, 4, 3, 4, 4, 8, 5, 7, 8, 10, 8, 13, 13, 20, 18, 25, 25, 36, 34, 48, 52, 64, 64, 85, 85, 108, 106, 129, 133, 160, 158, 189, 194, 229, 228, 276, 279, 332, 336, 394, 402, 476, 489, 572, 599, 699, 728, 845, 889, 1032, 1094, 1251, 1332, 1523
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OFFSET
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1,7
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LINKS
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EXAMPLE
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The a(13) = 8 partitions are (4441), (55111), (322222), (332221), (333211), (622111), (631111), (7111111).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], LCM@@#==Length[#]&]], {n, 30}]
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PROG
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(PARI) a(n) = {my(nb = 0); forpart(p=n, if (lcm(Vec(p))==#p, nb++); ); nb; } \\ Michel Marcus, Jul 03 2018
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CROSSREFS
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Cf. A067538, A074761, A143773, A285572, A289508, A290103, A305566, A316429, A316430, A316431, A316432.
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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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