A355784 - OEIS

%I #15 Jul 21 2022 07:45:35

%S 0,1,1,1,1,1,3,1,3,2,2,2,2,2,4,3,4,1,9,1,5,5,3,2,6,3,5,3,8,4,10,3,5,5,

%T 5,5,13,1,6,6,6,6,10,5,8,4,14,3,13,4,10,9,5,5,11,4,12,5,12,4,11,4,6,

%U 11,13,4,11,6,15,12,8,4,8,5,10,8,10,3,27,7,11,15,5,9,20,7,20,6,16,5,23

%N a(n) is the number of distinct primes of the form k*(n-k)+n where 1 <= k < n.

%H Robert Israel, <a href="/A355784/b355784.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7) = 3 because there are 3 such primes:

%e   1*6 + 7 = 13,

%e   2*5 + 7 = 17,

%e   3*4 + 7 = 19.

%p f:= proc(n) local k;

%p   nops(select(isprime, [seq(k*(n-k)+n,k=1..floor(n/2))]))

%p end proc:

%p map(f, [$1..100]);

%o (PARI) a(n) = vecsum(apply(isprime, Set(vector(n-1, k, k*(n-k)+n)))); \\ _Michel Marcus_, Jul 18 2022

%Y Cf. A355785.

%K nonn

%O 1,7

%A _J. M. Bergot_ and _Robert Israel_, Jul 16 2022