|
%I #10 Jun 15 2021 09:54:19
%S 0,1,1,1,1,4,1,0,0,5,1,4,1,4,4,0,1,4,1,3,3,3,1,3,0,4,0,3,1,4,1,0,3,3,
%T 3,3,1,3,2,3,1,4,1,2,4,3,1,3,0,3,3,3,1,2,2,2,3,3,1,4,1,2,4,0,3,5,1,2,
%U 2,4,1,3,1,3,3,2,2,5,1,2,0,2,1,3,3,4,2,3,1,3,2,3,2,2,2,2,1,3,2
%N a(n) is the number of distinct primes of the form n + A - B where A and B are sums of subsets of the prime factors of n.
%C If n is prime, a(n) = 1.
%C If n is a prime power other than 4, a(n) = 0.
%H Robert Israel, <a href="/A345300/b345300.txt">Table of n, a(n) for n = 1..10000</a>
%e a(6) = 4 because there are four such primes: 3 = 6-3, 5 = 6+2-3, 7 = 6+3-2, and 11=6+2+3.
%p f:= proc(n) local S, p;
%p S:= {n};
%p for p in numtheory:-factorset(n) do
%p S:= S union map(`+`,S,p) union map(`-`,S,p)
%p od:
%p nops(select(isprime,S))
%p end proc:
%p map(f, [$1..1000]);
%Y Cf. A345316.
%K nonn
%O 1,6
%A _J. M. Bergot_ and _Robert Israel_, Jun 13 2021
|
