A026728 a(n) = number of primes of the form k*(n-k) + 1.

0, 1, 1, 1, 2, 0, 3, 2, 1, 1, 4, 1, 6, 1, 1, 2, 8, 1, 5, 3, 1, 4, 7, 1, 7, 1, 4, 5, 8, 0, 10, 6, 2, 2, 7, 1, 9, 8, 4, 4, 14, 1, 16, 3, 3, 5, 12, 3, 7, 7, 4, 11, 21, 0, 11, 4, 7, 6, 11, 2, 12, 9, 7, 10, 7, 1, 22, 7, 7, 5, 17, 3, 23, 10, 2, 9, 19, 2, 19, 8, 5, 8, 23, 1, 16, 6, 4, 11, 14, 4, 16, 12, 9, 5, 12

Offset

1,5

Comments

Number of primes of form x*y+1 with x+y=n.

Links

Table of n, a(n) for n=1..95.

Example

a(7) = 3, 1*6 +1 = 7, 2*5 +1 = 11, 3*4 +1 = 13.
n=16: {m: m=x*y+1 and x+y=16} = {16,29,40,49,56,61,64,65} containing two primes: 29 and 61, therefore a(16)=2.
n = 7 is the only number which gives primes for all possible values of k.

Mathematica

a[n_] := Select[(Times @@ # + 1&) /@ IntegerPartitions[n, {2}], PrimeQ] // Length;
Array[a, 95] (* Jean-François Alcover, Aug 02 2018 *)

Prog

(PARI) { a(n)=local(r); r=0; for(k=1, n\2, if(isprime(k*(n-k)+1), r++)); r } (Alekseyev)

Crossrefs

Cf. A109904, A109905.

Sequence in context: A362328 A342176 A325195 * A241556 A242029 A090722

Adjacent sequences: A026725 A026726 A026727 * A026729 A026730 A026731

Keyword

nonn

Author

Reinhard Zumkeller, Jan 27 2004

Extensions

More terms from Max Alekseyev, Oct 04 2005

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

Status

approved