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A319825
LCM of the strict integer partition with FDH number n.
1
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).
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 28 2018
STATUS
approved