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

0,2

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Partial sums of A193433.

Cf. A000203, A002522, A006752.

Sequence in context: A367437 A367124 A222963 * A257028 A174938 A032248

Adjacent sequences: A333169 A333170 A333171 * A333173 A333174 A333175

Keyword

nonn

Author

Amiram Eldar, Mar 09 2020

Status

approved