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%I #16 Apr 19 2024 03:16:02
%S 1,3,6,9,13,17,21,27,33,37,43,49,53,61,71,76,82,88,94,106,114,118,126,
%T 138,144,152,164,170,178,186,192,204,212,220,238,247,251,259,275,283,
%U 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
%N a(n) = Sum_{i=1..n} tau(i)*tau(i+1)/2, where tau(n) = A000005(n) is the number of divisors of n.
%H Vincenzo Librandi, <a href="/A330321/b330321.txt">Table of n, a(n) for n = 1..5000</a>
%F From _Amiram Eldar_, Apr 19 2024: (Start)
%F a(n) = A330320(n)/2.
%F a(n) ~ (3/Pi^2) * n * log(n)^2. (End)
%t Accumulate[a[n_]:=DivisorSum[n, DivisorSigma[0, n+1] / 2 &]; Array[a, 68]] (* _Vincenzo Librandi_, Jan 11 2020 *)
%o (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
%Y Cf. A000005, A092517.
%Y Partial sums of A063123.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Dec 11 2019
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