A355784 a(n) is the number of distinct primes of the form k*(n-k)+n where 1 <= k < n.

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, 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, 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

Offset

1,7

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(7) = 3 because there are 3 such primes:
  1*6 + 7 = 13,
  2*5 + 7 = 17,
  3*4 + 7 = 19.

Maple

f:= proc(n) local k;
  nops(select(isprime, [seq(k*(n-k)+n, k=1..floor(n/2))]))
end proc:
map(f, [$1..100]);

Prog

(PARI) a(n) = vecsum(apply(isprime, Set(vector(n-1, k, k*(n-k)+n)))); \\ Michel Marcus, Jul 18 2022

Crossrefs

Cf. A355785.

Sequence in context: A357059 A326420 A171899 * A213885 A347739 A352931

Adjacent sequences: A355781 A355782 A355783 * A355785 A355786 A355787

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 16 2022

Status

approved