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 A026728 a(n) = number of primes of the form k*(n-k) + 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Number of primes of form x*y+1 with x+y=n. LINKS 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: 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

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Last modified April 10 22:20 EDT 2021. Contains 342856 sequences. (Running on oeis4.)