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

1,1

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