A330321 a(n) = Sum_{i=1..n} tau(i)*tau(i+1)/2, where tau(n) = A000005(n) is the number of divisors of n.

1, 3, 6, 9, 13, 17, 21, 27, 33, 37, 43, 49, 53, 61, 71, 76, 82, 88, 94, 106, 114, 118, 126, 138, 144, 152, 164, 170, 178, 186, 192, 204, 212, 220, 238, 247, 251, 259, 275, 283, 291, 299, 305, 323, 335, 339, 349, 364, 373, 385, 397, 403, 411, 427, 443, 459, 467, 471, 483, 495, 499, 511, 532, 546, 562, 570, 576, 588

Offset

1,2

Links

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

Formula

From Amiram Eldar, Apr 19 2024: (Start)

a(n) = A330320(n)/2.

a(n) ~ (3/Pi^2) * n * log(n)^2. (End)

Mathematica

Accumulate[a[n_]:=DivisorSum[n, DivisorSigma[0, n+1] / 2 &]; Array[a, 68]] (* Vincenzo Librandi, Jan 11 2020 *)

Prog

(PARI) lista(nmax) = {my(d1 = 1, d2, s = 0); for(k = 2, nmax, d2 = numdiv(k); s += (d1 * d2 / 2); print1(s, ", "); d1 = d2); } \\ Amiram Eldar, Apr 19 2024

Crossrefs

Cf. A000005, A092517.

Partial sums of A063123.

Sequence in context: A124288 A256966 A280944 * A205726 A002815 A342711

Adjacent sequences: A330318 A330319 A330320 * A330322 A330323 A330324

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 2019

Status

approved