A318588 Heinz numbers of integer partitions whose sum of reciprocals squared is an integer.

1, 2, 4, 8, 16, 32, 64, 81, 128, 162, 256, 324, 512, 648, 1024, 1296, 2048, 2592, 4096, 5184, 6561, 8192, 8775, 10368, 13122, 16384, 17550, 20736, 26244, 32768, 35100, 41472, 52488, 64827, 65536, 70200, 82944, 104976, 129654, 131072, 140400, 165888, 209952

Offset

1,2

Comments

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Links

Table of n, a(n) for n=1..43.

Example

Sequence of integer partitions whose Heinz numbers belong to the sequence begins: (), (1), (11), (111), (1111), (11111), (111111), (2222), (1111111), (22221), (11111111), (222211), (111111111), (2222111).

Mathematica

Select[Range[10000], IntegerQ[Total[If[#==1, {}, Cases[FactorInteger[#], {p_, k_}:>k/PrimePi[p]^2]]]]&]

Crossrefs

Cf. A001222, A056239, A058360, A112798, A289506, A289507, A316855, A316857.

Cf. A318584, A318585, A318586, A318587, A318589.

Sequence in context: A225878 A323097 A272985 * A008881 A208743 A335853

Adjacent sequences: A318585 A318586 A318587 * A318589 A318590 A318591

Keyword

nonn

Author

Gus Wiseman, Aug 29 2018

Status

approved