This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A299757 #5 Feb 23 2018 11:11:33
%S A299757 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,
%T A299757 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,
%U A299757 13,15,22,9,23,16,11,12,12,10,24,13,14,10,25,10,26,17
%N A299757 Weight of the strict integer partition with FDH number n.
%C A299757 Let f(n) = A050376(n) be the n-th Fermi-Dirac 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.
%C A299757 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.
%e A299757 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).
%t A299757 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)]]]]];
%t A299757 nn=200;FDprimeList=Array[FDfactor,nn,1,Union];
%t A299757 FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t A299757 Table[Total[FDfactor[n]/.FDrules],{n,nn}]
%Y A299757 Cf. A004111, A050376, A056239, A061775, A064547, A106400, A213925, A215366, A246867, A279065, A279614, A299090, A299755, A299756, A299758, A299759.
%K A299757 nonn
%O A299757 1,3
%A A299757 _Gus Wiseman_, Feb 18 2018