A316904 Heinz numbers of aperiodic integer partitions into relatively prime parts whose reciprocal sum is an integer.

2, 18, 72, 162, 195, 250, 288, 294, 390, 500, 588, 648, 780, 1125, 1152, 1176, 1458, 1560, 1755, 2000, 2250, 2352, 2592, 2646, 3120, 3185, 3510, 4000, 4500, 4608, 4704, 4802, 5292, 6240, 6370, 6475, 7020, 8450, 9000, 9408, 10125, 10368, 10527, 10584, 12480

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..45.

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), (221), (22111), (22221), (632), (3331), (2211111), (4421), (6321), (33311), (44211), (2222111).

Mathematica

Select[Range[2, 20000], And[GCD@@FactorInteger[#][[All, 2]]==1, GCD@@PrimePi/@FactorInteger[#][[All, 1]]==1, IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]]]&]

Crossrefs

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

Sequence in context: A258929 A034959 A316902 * A196812 A163102 A073976

Adjacent sequences: A316901 A316902 A316903 * A316905 A316906 A316907

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Status

approved