A316228 - OEIS

%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