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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
Sequence in context: A125853 A080025 A152111 * A324524 A325621 A025611
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 14 2018
STATUS
approved

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Last modified March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)