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

Author

Gus Wiseman, Aug 29 2018

Keywords

• nonn

Comments

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

Examples

			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).
		

Crossrefs

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

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

Programs

Mathematica

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