A300272 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

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).

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[#]&]

CROSSREFS

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

Sequence in context: A340931 A261416 A340386 * A352143 A365808 A344719

Adjacent sequences: A300269 A300270 A300271 * A300273 A300274 A300275

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 01 2018

STATUS

approved