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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.)