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 A330322 a(n) = Sum_{i=1..n} sigma(i)*sigma(i+1), where sigma(n) = A000203(n) is the sum of the divisors of n. 4
 3, 15, 43, 85, 157, 253, 373, 568, 802, 1018, 1354, 1746, 2082, 2658, 3402, 3960, 4662, 5442, 6282, 7626, 8778, 9642, 11082, 12942, 14244, 15924, 18164, 19844, 22004, 24308, 26324, 29348, 31940, 34532, 38900, 42358, 44638, 47998, 53038, 56818, 60850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 163. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 A. E. Ingham, Some asymptotic formulae in the theory of numbers, Journal of the London Mathematical Society, Vol. s1-2, No. 3 (1927), pp. 202-208. FORMULA a(n) ~ (5/6) * n^3. - Amiram Eldar, Mar 08 2020 MATHEMATICA f[n_] := DivisorSigma[1, n] * DivisorSigma[1, n + 1]; Accumulate @ Array[f, 100] (* Amiram Eldar, Mar 08 2020 *) Accumulate[Table[DivisorSigma[1, n*(n + 1)], {n, 1, 50}]] (* Vaclav Kotesovec, Aug 18 2021 *) CROSSREFS Cf. A000203. Partial sums of A083539. Sequence in context: A316642 A146805 A147057 * A101165 A127407 A196237 Adjacent sequences:  A330319 A330320 A330321 * A330323 A330324 A330325 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 12 2019 STATUS approved

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Last modified August 19 23:59 EDT 2022. Contains 356231 sequences. (Running on oeis4.)