

A299757


Weight of the strict integer partition with FDH number n.


35



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

1,3


COMMENTS

Let f(n) = A050376(n) be the nth FermiDirac prime. Every positive integer n has a unique factorization of the form n = f(s_1)*...*f(s_k) where the s_i are strictly increasing positive integers. This determines a unique strict integer partition (s_k...s_1) whose FDH number is then defined to be n.
In analogy with the Heinz number correspondence between integer partitions and positive integers (see A056239), FDH numbers give a correspondence between strict integer partitions and positive integers.


LINKS

Table of n, a(n) for n=1..74.


EXAMPLE

Sequence of strict integer partitions begins: () (1) (2) (3) (4) (2,1) (5) (3,1) (6) (4,1) (7) (3,2) (8) (5,1) (4,2) (9).


MATHEMATICA

FDfactor[n_]:=If[n===1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}>2^(m1)]]]]];
nn=200; FDprimeList=Array[FDfactor, nn, 1, Union];
FDrules=MapIndexed[(#1>#2[[1]])&, FDprimeList];
Table[Total[FDfactor[n]/.FDrules], {n, nn}]


CROSSREFS

Cf. A004111, A050376, A056239, A061775, A064547, A106400, A213925, A215366, A246867, A279065, A279614, A299090, A299755, A299756, A299758, A299759.
Sequence in context: A075850 A054437 A287821 * A159630 A305747 A304736
Adjacent sequences: A299754 A299755 A299756 * A299758 A299759 A299760


KEYWORD

nonn


AUTHOR

Gus Wiseman, Feb 18 2018


STATUS

approved



