

A026728


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


5



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
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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] (* JeanFrançois Alcover, Aug 02 2018 *)


PROG

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


CROSSREFS

Cf. A109904, A109905.
Sequence in context: A292108 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



