A327905 - OEIS

%I #6 Oct 01 2019 09:49:50

%S 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 52,55,56,57,58,62,63,66,68,70,74,75,76,77,80,82,84,86,88,91,93,94,95,

%U 96,98,99,100,104,106,110,112,114,116,118,122,123,125,126,132

%N FDH numbers of pairwise coprime sets.

%C 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 We use the Mathematica function CoprimeQ, meaning a singleton is not coprime unless it is {1}.

%H Wolfram Language Documentation, <a href="https://reference.wolfram.com/language/ref/CoprimeQ.html">CoprimeQ</a>

%e The sequence of terms together with their corresponding coprime sets begins:

%e    2: {1}

%e    6: {1,2}

%e    8: {1,3}

%e   10: {1,4}

%e   12: {2,3}

%e   14: {1,5}

%e   18: {1,6}

%e   20: {3,4}

%e   21: {2,5}

%e   22: {1,7}

%e   24: {1,2,3}

%e   26: {1,8}

%e   28: {3,5}

%e   32: {1,9}

%e   33: {2,7}

%e   34: {1,10}

%e   35: {4,5}

%e   38: {1,11}

%e   40: {1,3,4}

%e   42: {1,2,5}

%t 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 nn=100;FDprimeList=Array[FDfactor,nn,1,Union];

%t FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];

%t Select[Range[nn],CoprimeQ@@(FDfactor[#]/.FDrules)&]

%Y Heinz numbers of pairwise coprime partitions are A302696 (all), A302797 (strict), A302569 (with singletons), and A302798 (strict with singletons).

%Y FDH numbers of relatively prime sets are A319827.

%Y Cf. A050376, A056239, A064547, A213925, A259936, A299755, A299757, A304711, A319826, A326675.

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 30 2019