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Sorted list of Heinz numbers of odd partitions.
33

%I #8 Mar 03 2018 14:56:47

%S 2,5,8,11,17,20,23,31,32,41,44,47,50,59,67,68,73,80,83,92,97,103,109,

%T 110,124,125,127,128,137,149,157,164,167,170,176,179,188,191,197,200,

%U 211,227,230,233,236,241,242,257,268,269,272,275,277,283,292,307,310

%N Sorted list of Heinz numbers of odd partitions.

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

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

%e 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).

%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[100],OddQ[Total[primeMS[#]]]&&And@@OddQ/@primeMS[#]&]

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Mar 01 2018