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A316900 Heinz numbers of integer partitions into relatively prime parts whose reciprocal sum is an integer. 0
2, 4, 8, 16, 18, 32, 36, 64, 72, 128, 144, 162, 195, 250, 256, 288, 294, 324, 390, 500, 512, 576, 588, 648, 780, 1000, 1024, 1125, 1152, 1176, 1296, 1458, 1560, 1755, 2000, 2048, 2250, 2304, 2352, 2592, 2646, 2916, 3120, 3185, 3510, 4000, 4096, 4500, 4608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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..49.

Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums

EXAMPLE

The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (11), (111), (1111), (221), (11111), (2211), (111111), (22111), (1111111), (221111), (22221), (632), (3331), (11111111).

MATHEMATICA

Select[Range[2, 1000], And[GCD@@PrimePi/@FactorInteger[#][[All, 1]]==1, IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]]]&]

CROSSREFS

Cf. A000837, A002966, A051908, A058360, A100953, A289509, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Sequence in context: A226221 A072462 A088827 * A076057 A133809 A128700

Adjacent sequences:  A316897 A316898 A316899 * A316901 A316902 A316903

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 16 2018

STATUS

approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)