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A316228 Numbers whose Fermi-Dirac prime factorization sums to a Fermi-Dirac prime.

%I A316228 #10 Feb 02 2021 04:34:40
%S A316228 2,3,4,5,6,7,9,10,11,12,13,14,16,17,18,19,20,22,23,24,25,28,29,31,34,
%T A316228 36,37,39,40,41,43,46,47,48,49,52,53,55,56,58,59,61,63,66,67,71,73,76,
%U A316228 79,81,82,83,88,89,90,94,97,100,101,103,104,107,108,109,112
%N A316228 Numbers whose Fermi-Dirac prime factorization sums to a Fermi-Dirac prime.
%C A316228 A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0. Every positive integer has a unique factorization into distinct Fermi-Dirac primes.
%H A316228 Amiram Eldar, <a href="/A316228/b316228.txt">Table of n, a(n) for n = 1..10000</a>
%e A316228 Sequence of multiarrows in the form "number: sum <= factors" begins:
%e A316228    2:  2 <= {2}
%e A316228    3:  3 <= {3}
%e A316228    4:  4 <= {4}
%e A316228    5:  5 <= {5}
%e A316228    6:  5 <= {2,3}
%e A316228    7:  7 <= {7}
%e A316228    9:  9 <= {9}
%e A316228   10:  7 <= {2,5}
%e A316228   11: 11 <= {11}
%e A316228   12:  7 <= {3,4}
%e A316228   13: 13 <= {13}
%e A316228   14:  9 <= {2,7}
%e A316228   16: 16 <= {16}
%e A316228   17: 17 <= {17}
%e A316228   18: 11 <= {2,9}
%e A316228   19: 19 <= {19}
%e A316228   20:  9 <= {4,5}
%e A316228   22: 13 <= {2,11}
%e A316228   23: 23 <= {23}
%e A316228   24:  9 <= {2,3,4}
%t A316228 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 A316228 Select[Range[2,200],Length[FDfactor[Total[FDfactor[#]]]]==1&]
%Y A316228 Cf. A050376, A064547, A100118, A213925, A299757, A305829, A316202, A316210, A316211, A316220.
%K A316228 nonn
%O A316228 1,1
%A A316228 _Gus Wiseman_, Jun 27 2018