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.

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

Offset: 1

Author

N. J. A. Sloane, Dec 12 2019

Keywords

• nonn

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.

Crossrefs

Cf. A000203.

Partial sums of A083539.

Programs

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 *)

Formula

a(n) ~ (5/6) * n^3. - Amiram Eldar, Mar 08 2020