A331134 a(n) = Sum_{primes p <= n} r_2(p)/4, where r_2(n) = A004018(n).

0, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 21

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, A331135.

Programs

Mathematica

Accumulate[Table[If[PrimeQ[n], SquaresR[2, n], 0], {n, 1, 100}]/4] (* Amiram Eldar, Apr 23 2024 *)