A331135 a(n) = Sum_{primes p <= n} r_2(p-1)/4, where r_2(n) = A004018(n).
0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17
Offset: 1
Keywords
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).
Programs
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Mathematica
Accumulate[Table[If[PrimeQ[n], SquaresR[2, n-1], 0], {n, 1, 100}]/4] (* Amiram Eldar, Apr 23 2024 *)