A316890 Heinz numbers of integer partitions into relatively prime parts whose reciprocal sum is 1.

2, 195, 3185, 6475, 10527, 16401, 20445, 20535, 21045, 25365, 46155, 164255, 171941, 218855, 228085, 267883, 312785, 333925, 333935, 335405, 343735, 355355, 414295, 442975, 474513, 527425, 549575, 607475, 633777, 691041, 711321, 722425, 753865, 804837, 822783

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).

Includes 29888089, which is the first perfect power in the sequence and is absent from A316888.

Links

Table of n, a(n) for n=1..35.

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

Mathematica

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

Crossrefs

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

Sequence in context: A103429 A316901 A316888 * A143659 A282700 A256410

Adjacent sequences: A316887 A316888 A316889 * A316891 A316892 A316893

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Status

approved