A300272 Sorted list of Heinz numbers of odd partitions.

2, 5, 8, 11, 17, 20, 23, 31, 32, 41, 44, 47, 50, 59, 67, 68, 73, 80, 83, 92, 97, 103, 109, 110, 124, 125, 127, 128, 137, 149, 157, 164, 167, 170, 176, 179, 188, 191, 197, 200, 211, 227, 230, 233, 236, 241, 242, 257, 268, 269, 272, 275, 277, 283, 292, 307, 310

Offset: 1

Author

Gus Wiseman, Mar 01 2018

Keywords

• nonn

Comments

An odd partition is an integer partition of an odd number into an odd number of parts, all of which are odd.

Any product of three members of this sequence is also in the sequence.

Examples

			Sequence of odd partitions begins: (1), (3), (111), (5), (7), (311), (9), (11), (11111), (13), (511), (15), (331), (17), (19), (711), (21), (31111), (23), (911), (25), (27), (29), (531), (1111), (333), (31), (1111111).
		

Crossrefs

Cf. A000009, A031368, A066208, A078408, A094457, A215366, A299757, A300063.

Programs

Mathematica

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],OddQ[Total[primeMS[#]]]&&And@@OddQ/@primeMS[#]&]