A316889 - OEIS

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A316889

Heinz numbers of aperiodic integer partitions whose reciprocal sum is 1.

2, 147, 195, 3185, 6475, 6591, 7581, 10101, 10527, 16401, 20445, 20535, 21045, 25365, 46155, 107653, 123823, 142805, 164255, 164983, 171941, 218855, 228085, 267883, 304175, 312785, 333925, 333935, 335405, 343735, 355355, 390963, 414295, 442975, 444925, 455975

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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).

A partition is aperiodic if its multiplicities are relatively prime.

LINKS

Table of n, a(n) for n=1..36.

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

EXAMPLE

Sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (4,4,2), (6,3,2), (6,4,4,3), (12,4,3,3), (6,6,6,2), (8,8,4,2), (12,6,4,2), (10,5,5,2), (20,5,4,2), (15,10,3,2), (12,12,3,2), (18,9,3,2), (24,8,3,2), (42,7,3,2).

MATHEMATICA

Select[Range[2, 100000], And[GCD@@FactorInteger[#][[All, 2]]==1, Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]==1]&]

CROSSREFS

Cf. A000837, A002966, A007916, A051908, A058360, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Sequence in context: A182478 A214910 A328228 * A251863 A110624 A177319

Adjacent sequences: A316886 A316887 A316888 * A316890 A316891 A316892

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 16 2018

STATUS

approved