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 A316856 Heinz numbers of integer partitions whose reciprocal sum is an integer. 20
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). LINKS EXAMPLE 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). MATHEMATICA Select[Range[1000], IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]], {m, If[#==1, {}, FactorInteger[#]]}]]&] CROSSREFS 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 KEYWORD nonn AUTHOR Gus Wiseman, Jul 14 2018 STATUS approved

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Last modified August 11 07:36 EDT 2022. Contains 356055 sequences. (Running on oeis4.)