A331136 a(n) = Sum_{primes p < n} r_2(n-p)/4, where r_2(n) = A004018(n).

0, 0, 1, 2, 1, 2, 4, 3, 2, 3, 3, 6, 4, 2, 7, 5, 3, 6, 5, 7, 7, 7, 7, 7, 5, 3, 10, 10, 6, 8, 9, 9, 9, 7, 4, 13, 9, 6, 15, 7, 7, 14, 11, 10, 11, 9, 12, 16, 9, 7, 12, 13, 11, 15, 14, 13, 17, 12, 7, 16, 11, 8, 23, 12, 9, 17, 14, 16, 18, 15, 15, 21, 12, 10, 17, 19, 16, 20, 16, 11, 22, 15, 14, 27, 14, 11, 29, 20, 12, 18

Offset: 1

Author

N. J. A. Sloane, Jan 11 2020

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Yoichi Motohashi, On the distribution of prime numbers which are of the form x^2+y^2+1, Acta Arith. 16 (1969/70), 351-363. MR0288086 (44 #5284).

Crossrefs

Cf. A004018, A331134.

Programs

Mathematica

a[n_] := Sum[SquaresR[2, n - p]/4, {p, Select[Range[n - 1], PrimeQ]}]; Array[a, 100] (* Amiram Eldar, Apr 23 2024 *)