This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362985 #5 May 12 2023 04:26:21
%S A362985 2,4,8,2,1,7,9,1,9,6,4,2,2,3,5,9,5,2,5,4,6,1,6,7,6,4,3,6,7,4,6,8,7,6,
%T A362985 9,8,5,3,6,3,6,8,9,4,0,9,7,1,9,3,0,4,6,8,3,5,4,3,6,3,9,3,2,8,1,4,4,4,
%U A362985 2,3,3,8,8,5,7,6,7,5,0,4,6,3,4,1,1,5,0,7,3,1,0,3,9,8,0,4,4,7,4,0,3,7,3,1,0
%N A362985 Decimal expansion of the asymptotic mean of the abundancy index of the cubefull numbers (A036966).
%H A362985 Rafael Jakimczuk and Matilde Lalín, <a href="https://doi.org/10.7546/nntdm.2022.28.4.617-634">Asymptotics of sums of divisor functions over sequences with restricted factorization structure</a>, Notes on Number Theory and Discrete Mathematics, Vol. 28, No. 4 (2022), pp. 617-634, eq. (6).
%F A362985 Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A362986(k)/A036966(k).
%F A362985 Equals zeta(4/3) * Product_{p prime} ((p^5 + p^(10/3) + p^3 + p^(8/3) - 1)/(p^(10/3) * (p^(5/3) + p^(1/3) + 1))).
%e A362985 2.48217919642235952546167643674687698536368940971930468354...
%t A362985 $MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{2, -1, -2, 3, -2, -1, 3, -2, -2, 3, -1, -2, 3, -1, -1, 1}, {0, 0, 0, -4, 0, 6, 7, 4, 9, 0, -11, -22, -26, -21, -15, 20}, m]; RealDigits[((2^5 + 2^(10/3) + 2^3 + 2^(8/3) - 1)/(2^(10/3)*(2^(5/3) + 2^(1/3) + 1)))*((3^5 + 3^(10/3) + 3^3 + 3^(8/3) - 1)/(3^(10/3)*(3^(5/3) + 3^(1/3) + 1))) * Zeta[4/3] * Exp[NSum[Indexed[c, n]*(PrimeZetaP[n/3] - 1/2^(n/3) - 1/3^(n/3))/n, {n, 4, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 120][[1]]
%o A362985 (PARI) zeta(4/3) * prodeulerrat((p^15 + p^10 + p^9 + p^8 - 1)/(p^10 * (p^5 + p + 1)), 1/3)
%Y A362985 Cf. A000203, A036966, A017665, A017666, A362986.
%Y A362985 Similar constants (the asymptotic mean of the abundancy index of other sequences): A013661 (all positive integers), A082020 (cubefree), A111003 (odd), A157292 (5-free), A157294 (7-free), A157296 (9-free), A245058 (even), A240976 (squares), A306633 (squarefree), A362984 (powerful).
%K A362985 nonn,cons
%O A362985 1,1
%A A362985 _Amiram Eldar_, May 12 2023