A316888 Heinz numbers of aperiodic 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).

A partition is aperiodic if its multiplicities are relatively prime.

Does not contain 29888089, which belongs to A316890 and is the Heinz number of a periodic partition.

Links

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

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

Example

The partition (6,4,4,3) with Heinz number 3185 is aperiodic, has relatively prime parts, and 1/6 + 1/4 + 1/4 + 1/3 = 1, so 3185 belongs to the sequence.
The sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (6,3,2), (6,4,4,3), (12,4,3,3), (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, GCD@@PrimePi/@FactorInteger[#][[All, 1]]==1, Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]==1]&]

Crossrefs

Cf. A000837, A002966, A007916, A051908, A100953, A289509, A296150, A316855, A316856, A316857, A316888-A316904.

Sequence in context: A229017 A103429 A316901 * A316890 A143659 A282700

Adjacent sequences: A316885 A316886 A316887 * A316889 A316890 A316891

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Status

approved