A316776 a(n) is the number of integers 0 < k < n such that n^2 - k^2 is a semiprime.

0, 0, 0, 1, 2, 1, 1, 3, 2, 2, 3, 3, 3, 2, 3, 2, 4, 5, 1, 4, 4, 3, 3, 5, 5, 4, 5, 4, 4, 6, 2, 5, 7, 2, 6, 6, 4, 5, 8, 4, 4, 8, 5, 5, 9, 5, 5, 8, 3, 6, 8, 5, 5, 8, 6, 8, 10, 7, 5, 13, 4, 6, 10, 3, 8, 9, 6, 5, 8, 7, 8, 12, 6, 5, 12, 4, 8, 12, 4, 9, 11, 5, 5, 13, 10, 6, 11, 7, 7, 14, 6, 9, 14, 6, 8, 11

Offset: 1

Author

Arnauld Chevallier, Jul 12 2018

Keywords

• nonn

Examples

			a(11) = 3 because 11^2 - 6^2 = 85, 11^2 - 8^2 = 57 and 11^2 - 10^2 = 21 are the only three semiprimes of the form 11^2 - k^2 with 0 < k < 11.
		

Crossrefs

Cf. A001358.

Programs

Mathematica

a[n_] := Sum[Boole[ PrimeOmega[n^2 - k^2] == 2], {k, n-1}]; Array[a, 96] (* Giovanni Resta, Jul 13 2018 *)

PARI

a(n) = sum(k=1, n-1, bigomega(n^2-k^2)==2); \\ Michel Marcus, Jul 12 2018