A316094 FDH numbers of strict integer partitions with odd parts.

1, 2, 4, 7, 8, 11, 14, 16, 19, 22, 25, 28, 31, 32, 38, 41, 44, 47, 50, 53, 56, 61, 62, 64, 71, 76, 77, 79, 82, 83, 88, 94, 97, 100, 101, 103, 106, 107, 109, 112, 113, 121, 122, 124, 127, 128, 131, 133, 137, 139, 142, 149, 151, 152, 154, 157, 158, 163, 164, 166

Offset

1,2

Comments

Also numbers n such that A305829(n) is odd.

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH number of a strict integer partition (y_1,...,y_k) is f(y_1)*...*f(y_k).

Links

Table of n, a(n) for n=1..60.

Example

Sequence of all integer partitions with distinct odd parts begins (), (1), (3), (5), (3,1), (7), (5,1), (9), (11), (7,1), (13), (5,3), (15), (9,1), (11,1), (17), (7,3), (19), (13,1), (21), (5,3,1), (23), (15,1), (9,3), (25), (11,3), (7,5), (27), (17,1), (29), (7,3,1), (19,1), (31).

Mathematica

nn=100;
FDfactor[n_]:=If[n==1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];
FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Select[Range[nn], OddQ[Times@@(FDfactor[#]/.FDrules)]&]

Crossrefs

Cf. A000700, A050376, A064547, A213925, A258116, A279065, A299755, A299757, A305829.

Sequence in context: A288307 A286060 A080704 * A290259 A244779 A162158

Adjacent sequences: A316091 A316092 A316093 * A316095 A316096 A316097

Keyword

nonn

Author

Gus Wiseman, Jun 24 2018

Status

approved