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