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A339438 Composite numbers k such that k + A339436(k) is prime.

%I A339438 #11 Feb 06 2021 22:08:32
%S A339438 6,10,14,15,20,21,24,26,33,34,35,38,40,44,46,51,52,55,57,58,63,65,74,
%T A339438 76,85,86,88,90,92,93,96,111,117,118,123,124,135,136,141,143,145,147,
%U A339438 150,153,155,158,161,164,166,172,177,178,180,184,185,194,198,201,203,205,206,207,208,209,215,221
%N A339438 Composite numbers k such that k + A339436(k) is prime.
%C A339438 If n = p_1 * ... * p_m with primes p_i <= p_{i+1}, then p_1 + p_1*p_2 + ... + p_1*p_2*...*p_m + p2*...*p_m + ... + p_m is prime.
%H A339438 Robert Israel, <a href="/A339438/b339438.txt">Table of n, a(n) for n = 1..10000</a>
%e A339438 a(5)=20 is a term because 20=2*2*5 and 2+2*2+2*2*5+2*5+5 = 41 is prime.
%p A339438 filter:= proc(n) local L,m;
%p A339438   L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));
%p A339438   m:= nops(L);
%p A339438   if m=1 then return false fi;
%p A339438   isprime(n + add(mul(L[i],i=1..j)+mul(L[i],i=j+1..m),j=1..m-1))
%p A339438 end proc:
%p A339438 select(filter, [$4..300]);
%Y A339438 Includes A088709.
%Y A339438 Cf. A339436, A339437.
%K A339438 nonn
%O A339438 1,1
%A A339438 _J. M. Bergot_ and _Robert Israel_, Dec 04 2020