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A331133
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a(n) = Sum_{i=1..n} d(i)^2*d(i+1)/2, where d(n) = A000005(n).
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2
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1, 5, 11, 20, 28, 44, 52, 76, 94, 110, 122, 158, 166, 198, 238, 263, 275, 311, 323, 395, 427, 443, 459, 555, 573, 605, 653, 689, 705, 769, 781, 853, 885, 917, 989, 1070, 1078, 1110, 1174, 1238, 1254, 1318, 1330, 1438, 1510, 1526, 1546, 1696, 1723, 1795, 1843, 1879, 1895, 2023, 2087, 2215, 2247, 2263, 2287, 2431
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ (c/(2*Pi^2)) * n * log(n)^4, where c = Product_{p prime} (1 - 1/p + (1/p)*(1 - 1/p)^2*(1 + 1/p)^(-1)) = 0.35823163000196141456... . (End)
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MATHEMATICA
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Accumulate[a[n_]:=DivisorSum[n+1, DivisorSigma[0, n]^2 &]/2; Array[a, 60]] (* Vincenzo Librandi, Jan 12 2020 *)
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PROG
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(Magma) [&+[#Divisors(i)^2*#Divisors(i+1)/2:i in [1..n]]:n in [1..60]]; // Marius A. Burtea, Jan 12 2020
(PARI) lista(nmax) = {my(d1 = 1, d2, s = 0); for(n = 2, nmax, d2 = numdiv(n); s += d1^2 * d2; print1(s/2, ", "); d1 = d2); } \\ Amiram Eldar, Apr 23 2024
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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