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A316856
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Heinz numbers of integer partitions whose reciprocal sum is an integer.
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20
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1, 2, 4, 8, 9, 16, 18, 32, 36, 64, 72, 81, 125, 128, 144, 147, 162, 195, 250, 256, 288, 294, 324, 390, 500, 512, 576, 588, 648, 729, 780, 1000, 1024, 1125, 1152, 1176, 1296, 1323, 1458, 1560, 1755, 2000, 2048, 2250, 2304, 2352, 2401, 2592, 2646, 2916, 3120
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OFFSET
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1,2
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COMMENTS
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The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
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LINKS
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Table of n, a(n) for n=1..51.
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EXAMPLE
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195 is the Heinz number of (6,3,2), which has reciprocal sum 1/6 + 1/3 + 1/2 = 1, which is an integer, so 195 belongs to the sequence.
The sequence of all integer partitions whose reciprocal sum is an integer begins: (), (1), (11), (111), (22), (1111), (221), (11111), (2211), (111111), (22111), (2222).
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MATHEMATICA
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Select[Range[1000], IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]], {m, If[#==1, {}, FactorInteger[#]]}]]&]
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CROSSREFS
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Cf. A000041, A051908, A056239, A058360, A072411, A296150, A316854, A316855, A316857.
Sequence in context: A125853 A080025 A152111 * A324524 A325621 A025611
Adjacent sequences: A316853 A316854 A316855 * A316857 A316858 A316859
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Jul 14 2018
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STATUS
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approved
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