A330320 -id:A330320 - cp's OEIS frontend

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

N. J. A. Sloane, Dec 11 2019

nonn

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

Cf. A000005, A092517.

Partial sums of A063123.

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

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

From Amiram Eldar, Apr 19 2024: (Start)
a(n) = A330320(n)/2.
a(n) ~ (3/Pi^2) * n * log(n)^2. (End)

A331079 a(n) = Sum_{i=1..n} u_2(i)*u_2(i+1), where u_2(n) = A038548(n).

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 12, 16, 20, 22, 25, 28, 30, 34, 40, 43, 46, 49, 52, 58, 62, 64, 68, 76, 80, 84, 90, 93, 97, 101, 104, 110, 114, 118, 128, 133, 135, 139, 147, 151, 155, 159, 162, 171, 177, 179, 184, 194, 200, 206, 212, 215, 219, 227, 235, 243, 247, 249, 255, 261

Offset: 1

N. J. A. Sloane, Jan 10 2020

nonn

For background references see A330570.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A038548, A330320.

With[{s = Table[Ceiling[DivisorSigma[0, n] / 2], {n, 1, 100}]}, Accumulate[Most[s] * Rest[s]]] (* Amiram Eldar, Apr 19 2024 *)

cp's OEIS Frontend

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.

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