A319827 FDH numbers of relatively prime strict integer partitions.

2, 6, 8, 10, 12, 14, 18, 20, 21, 22, 24, 26, 28, 30, 32, 33, 34, 35, 38, 40, 42, 44, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 66, 68, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112

Offset

1,1

Comments

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..64.

Example

The sequence of all relatively prime strict integer partitions begins: (1), (2,1), (3,1), (4,1), (3,2), (5,1), (6,1), (4,3), (5,2), (7,1), (3,2,1), (8,1), (5,3), (4,2,1).

Mathematica

nn=200;
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], GCD@@(FDfactor[#]/.FDrules)==1&]

Crossrefs

Cf. A050376, A056239, A064547, A213925, A289508, A289509, A290103, A299755, A299757, A319826.

Sequence in context: A198832 A173634 A005795 * A327905 A157502 A216032

Adjacent sequences: A319824 A319825 A319826 * A319828 A319829 A319830

Keyword

nonn

Author

Gus Wiseman, Sep 28 2018

Status

approved