A319825 LCM of the strict integer partition with FDH number n.

0, 1, 2, 3, 4, 2, 5, 3, 6, 4, 7, 6, 8, 5, 4, 9, 10, 6, 11, 12, 10, 7, 12, 6, 13, 8, 6, 15, 14, 4, 15, 9, 14, 10, 20, 6, 16, 11, 8, 12, 17, 10, 18, 21, 12, 12, 19, 18, 20, 13, 10, 24, 21, 6, 28, 15, 22, 14, 22, 12, 23, 15, 30, 9, 8, 14, 24, 30, 12, 20, 25, 6, 26

Offset

1,3

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..73.

Example

45 is the FDH number of (6,4), which has LCM 12, so a(45) = 12.

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];
LCM@@@Table[Reverse[FDfactor[n]/.FDrules], {n, 2, nn}]

Crossrefs

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

Sequence in context: A364950 A100798 A302785 * A305829 A121701 A161759

Adjacent sequences: A319822 A319823 A319824 * A319826 A319827 A319828

Keyword

nonn

Author

Gus Wiseman, Sep 28 2018

Status

approved