A330322 - OEIS

%I #13 Aug 18 2021 06:16:28

%S 3,15,43,85,157,253,373,568,802,1018,1354,1746,2082,2658,3402,3960,

%T 4662,5442,6282,7626,8778,9642,11082,12942,14244,15924,18164,19844,

%U 22004,24308,26324,29348,31940,34532,38900,42358,44638,47998,53038,56818,60850

%N a(n) = Sum_{i=1..n} sigma(i)*sigma(i+1), where sigma(n) = A000203(n) is the sum of the divisors of n.

%D Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 163.

%H Amiram Eldar, <a href="/A330322/b330322.txt">Table of n, a(n) for n = 1..10000</a>

%H A. E. Ingham, <a href="https://doi.org/10.1112/jlms/s1-2.3.202">Some asymptotic formulae in the theory of numbers</a>, Journal of the London Mathematical Society, Vol. s1-2, No. 3 (1927), pp. 202-208.

%F a(n) ~ (5/6) * n^3. - _Amiram Eldar_, Mar 08 2020

%t f[n_] := DivisorSigma[1, n] * DivisorSigma[1, n + 1]; Accumulate @ Array[f, 100] (* _Amiram Eldar_, Mar 08 2020 *)

%t Accumulate[Table[DivisorSigma[1, n*(n + 1)], {n, 1, 50}]] (* _Vaclav Kotesovec_, Aug 18 2021 *)

%Y Cf. A000203.

%Y Partial sums of A083539.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 12 2019