A333168 a(n) = Sum_{k=0..n} r_2(k^2 + 1), where r_2(k) is the number of ways of writing k as a sum of 2 squares (A004018).

4, 8, 16, 24, 32, 40, 48, 60, 76, 84, 92, 100, 116, 132, 140, 148, 156, 172, 196, 204, 212, 228, 244, 260, 268, 276, 284, 300, 316, 324, 340, 356, 380, 396, 412, 420, 428, 444, 468, 476, 484, 496, 512, 536, 552, 560, 576, 608, 624, 632, 648, 656, 672, 688, 696

Offset: 0

Author

Amiram Eldar, Mar 09 2020

Keywords

• nonn

Examples

			a(0) = r_2(0^2 + 1) = r_2(1) = A004018(1) = 4.
a(1) = r_2(0^2 + 1) + r_2(1^1 + 1) = r_2(1) + r_2(2) = A004018(1) + A004018(2) = 4 + 4 = 8.
		

References

• Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• E. J. Scourfield, The divisors of a quadratic polynomial, Glasgow Mathematical Journal, Vol. 5, No. 1 (1961), pp. 8-20.

Crossrefs

Partial sums of A333167.

Cf. A002522, A004018.

Programs

Mathematica

Accumulate @ Table[SquaresR[2, k^2 + 1], {k, 0, 100}]

Formula

a(n) ~ (8/Pi) * n * log(n).