A316902 Heinz numbers of aperiodic integer partitions whose reciprocal sum is an integer.

2, 18, 72, 147, 162, 195, 250, 288, 294, 390, 500, 588, 648, 780, 1125, 1152, 1176, 1323, 1458, 1560, 1755, 2000, 2250, 2352, 2592, 2646, 3120, 3185, 3510, 4000, 4500, 4608, 4704, 4802, 5292, 6240, 6370, 6475, 6591, 7020, 7581, 8450, 9000, 9408, 10101, 10125

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..46.

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), (442), (22221), (632), (3331), (2211111), (4421), (6321), (33311), (44211), (2222111).

Mathematica

Select[Range[2, 20000], And[GCD@@FactorInteger[#][[All, 2]]==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: A242200 A258929 A034959 * A316904 A196812 A163102

Adjacent sequences: A316899 A316900 A316901 * A316903 A316904 A316905

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Status

approved