A330320 a(n) = Sum_{i=1..n} tau(i)*tau(i+1), where tau(n) = A000005(n) is the number of divisors of n.

2, 6, 12, 18, 26, 34, 42, 54, 66, 74, 86, 98, 106, 122, 142, 152, 164, 176, 188, 212, 228, 236, 252, 276, 288, 304, 328, 340, 356, 372, 384, 408, 424, 440, 476, 494, 502, 518, 550, 566, 582, 598, 610, 646, 670, 678, 698, 728, 746, 770, 794, 806, 822, 854, 886, 918, 934, 942, 966, 990, 998, 1022, 1064, 1092, 1124, 1140

Offset

1,1

Comments

For background references see A330570.

References

József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 61.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

A. E. Ingham, Some asymptotic formulae in the theory of numbers, Journal of the London Mathematical Society, Vol. 1, No. 3 (1927), pp. 202-208.

Nikolay V. Kuznetsov, Convolution of the Fourier coefficients of the Eisenstein-Maass series, Journal of Soviet Mathematics, Vol. 29, No. 2 (1985), pp. 1131-1159.

Formula

a(n) ~ (1/zeta(2)) * n * log(n)^2. - Amiram Eldar, Mar 05 2020

Mathematica

Accumulate[a[n_]:=DivisorSum[n+1, DivisorSigma[0, n]&]; Array[a, 66]] (* Vincenzo Librandi, Jan 10 2020 *)
Accumulate[Times@@@Partition[DivisorSigma[0, Range[70]], 2, 1]] (* Harvey P. Dale, Nov 02 2023 *)

Prog

(PARI) a(n) = sum(i=1, n, numdiv(i*(i+1))); \\ Michel Marcus, Jan 11 2020

Crossrefs

Cf. A000005, A059956, A063123.

Partial sums of A092517.

Sequence in context: A276829 A032371 A162802 * A267461 A108585 A294062

Adjacent sequences: A330317 A330318 A330319 * A330321 A330322 A330323

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 2019

Status

approved