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A300486
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Number of relatively prime or monic partitions of n.
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17
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1, 2, 3, 4, 7, 8, 15, 18, 28, 35, 56, 64, 101, 120, 168, 210, 297, 348, 490, 583, 776, 946, 1255, 1482, 1952, 2335, 2981, 3581, 4565, 5387, 6842, 8119, 10086, 12013, 14863, 17527, 21637, 25525, 31083, 36695, 44583, 52256, 63261, 74171, 88932, 104303, 124754
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OFFSET
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1,2
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COMMENTS
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A relatively prime or monic partition of n is an integer partition of n that is either of length 1 (monic) or whose parts have no common divisor other than 1 (relatively prime).
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LINKS
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FORMULA
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EXAMPLE
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The a(6) = 8 relatively prime or monic partitions are (6), (51), (411), (321), (3111), (2211), (21111), (111111). Missing from this list are (42), (33), (222).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Or[Length[#]===1, GCD@@#===1]&]], {n, 20}]
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PROG
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(PARI) a(n)={(n > 1) + sumdiv(n, d, moebius(d)*numbpart(n/d))} \\ Andrew Howroyd, Aug 29 2018
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CROSSREFS
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Cf. A000837, A001383, A063834, A093637, A196545, A281113, A289501, A300383, A301462, A301467, A301480, A302094, A302698, A302915, A302916, A302917.
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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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