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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
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 163.
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 12 2019
STATUS
approved