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A327905 FDH numbers of pairwise coprime sets.

%I A327905 #6 Oct 01 2019 09:49:50
%S A327905 2,6,8,10,12,14,18,20,21,22,24,26,28,32,33,34,35,38,40,42,44,46,48,50,
%T A327905 52,55,56,57,58,62,63,66,68,70,74,75,76,77,80,82,84,86,88,91,93,94,95,
%U A327905 96,98,99,100,104,106,110,112,114,116,118,122,123,125,126,132
%N A327905 FDH numbers of pairwise coprime sets.
%C A327905 Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH-number of a strict partition or finite set {y_1,...,y_k} is f(y_1)*...*f(y_k).
%C A327905 We use the Mathematica function CoprimeQ, meaning a singleton is not coprime unless it is {1}.
%H A327905 Wolfram Language Documentation, <a href="https://reference.wolfram.com/language/ref/CoprimeQ.html">CoprimeQ</a>
%e A327905 The sequence of terms together with their corresponding coprime sets begins:
%e A327905    2: {1}
%e A327905    6: {1,2}
%e A327905    8: {1,3}
%e A327905   10: {1,4}
%e A327905   12: {2,3}
%e A327905   14: {1,5}
%e A327905   18: {1,6}
%e A327905   20: {3,4}
%e A327905   21: {2,5}
%e A327905   22: {1,7}
%e A327905   24: {1,2,3}
%e A327905   26: {1,8}
%e A327905   28: {3,5}
%e A327905   32: {1,9}
%e A327905   33: {2,7}
%e A327905   34: {1,10}
%e A327905   35: {4,5}
%e A327905   38: {1,11}
%e A327905   40: {1,3,4}
%e A327905   42: {1,2,5}
%t A327905 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 A327905 nn=100;FDprimeList=Array[FDfactor,nn,1,Union];
%t A327905 FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t A327905 Select[Range[nn],CoprimeQ@@(FDfactor[#]/.FDrules)&]
%Y A327905 Heinz numbers of pairwise coprime partitions are A302696 (all), A302797 (strict), A302569 (with singletons), and A302798 (strict with singletons).
%Y A327905 FDH numbers of relatively prime sets are A319827.
%Y A327905 Cf. A050376, A056239, A064547, A213925, A259936, A299755, A299757, A304711, A319826, A326675.
%K A327905 nonn
%O A327905 1,1
%A A327905 _Gus Wiseman_, Sep 30 2019