A333172 a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).

1, 4, 10, 28, 46, 88, 126, 219, 303, 429, 531, 717, 897, 1221, 1419, 1761, 2019, 2559, 2993, 3539, 3941, 4697, 5285, 6257, 6835, 7777, 8455, 9787, 10735, 12001, 12973, 14569, 15871, 17851, 19111, 20953, 22251, 24735, 26577, 28863, 30465, 33078, 35202, 38736

Offset: 0

Author

Amiram Eldar, Mar 09 2020

Keywords

• nonn

Examples

			a(0) = sigma(0^2 + 1) = sigma(1) = 1.
a(1) = sigma(0^2 + 1) + sigma(1^2 + 1) = sigma(1) + sigma(2) = 1 + 3 = 4.
		

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

Crossrefs

Partial sums of A193433.

Cf. A000203, A002522, A006752.

Programs

Mathematica

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

PARI

a(n) = sum(k=0, n, sigma(k^2+1)); \\ Michel Marcus, Mar 10 2020

Formula

a(n) ~ (5*G/Pi^2) * n^3, where G is Catalan's constant (A006752).