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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

Table of n, a(n) for n=1..51.

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 February 20 14:03 EST 2020. Contains 332078 sequences. (Running on oeis4.)