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A333172 a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A222453 A186278 A222963 * A257028 A174938 A032248

Adjacent sequences:  A333169 A333170 A333171 * A333173 A333174 A333175

KEYWORD

nonn

AUTHOR

Amiram Eldar, Mar 09 2020

STATUS

approved

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Last modified September 17 14:07 EDT 2021. Contains 347478 sequences. (Running on oeis4.)