cp's OEIS Frontend

A316265 FDH numbers of strict integer partitions with prime parts.

%I A316265 #6 Jun 29 2018 11:35:18
%S A316265 1,3,4,7,11,12,19,21,25,28,33,41,44,47,57,61,75,76,77,83,84,97,100,
%T A316265 121,123,132,133,139,141,151,164,169,175,183,188,197,209,228,231,233,
%U A316265 241,244,249,271,275,287,289,291,300,307,308,329,332,347,361,363,388
%N A316265 FDH numbers of strict integer partitions with prime parts.
%C A316265 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).
%e A316265 Sequence of strict integer partitions with prime parts, preceded by their FDH numbers, begins:
%e A316265    1: ()
%e A316265    3: (2)
%e A316265    4: (3)
%e A316265    7: (5)
%e A316265   11: (7)
%e A316265   12: (3,2)
%e A316265   19: (11)
%e A316265   21: (5,2)
%e A316265   25: (13)
%e A316265   28: (5,3)
%e A316265   33: (7,2)
%e A316265   41: (17)
%e A316265   44: (7,3)
%e A316265   47: (19)
%e A316265   57: (11,2)
%e A316265   61: (23)
%e A316265   75: (13,2)
%e A316265   76: (11,3)
%e A316265   77: (7,5)
%e A316265   83: (29)
%e A316265   84: (5,3,2)
%t A316265 nn=100;
%t A316265 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 A316265 FDprimeList=Array[FDfactor,nn,1,Union];FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t A316265 Select[Range[nn],And@@PrimeQ/@(FDfactor[#]/.FDrules)&]
%Y A316265 Cf. A000586, A045450, A050376, A064547, A213925, A299755, A299757, A316185, A316266, A316267.
%K A316265 nonn
%O A316265 1,2
%A A316265 _Gus Wiseman_, Jun 28 2018