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

0,1

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.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Partial sums of A333167.

Cf. A002522, A004018.

Sequence in context: A097057 A347931 A354810 * A306219 A160746 A160740

Adjacent sequences: A333165 A333166 A333167 * A333169 A333170 A333171

Keyword

nonn

Author

Amiram Eldar, Mar 09 2020

Status

approved