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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
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
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
Partial sums of A063123.
Sequence in context: A124288 A256966 A280944 * A205726 A002815 A342711
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 11 2019
STATUS
approved