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 A328013 #18 Dec 26 2024 20:02:07
%S A328013 3,5,1,9,5,5,5,0,5,8,4,1,7,1,0,6,6,4,7,1,9,7,5,2,9,4,0,3,6,9,8,5,7,8,
%T A328013 1,7,1,8,6,0,3,9,8,0,8,2,2,5,4,0,7,8,1,4,7,1,1,4,6,4,0,3,1,4,5,4,1,7,
%U A328013 8,3,9,8,4,7,9,7,3,5,4,0,8,9,7,7,1,3,5,8,0,3,7,5,3,6,4,6,1,6,2,0,1,1,4,5,5
%N A328013 Decimal expansion of the growth constant for the partial sums of powerful part of n (A057521).
%D A328013 D. Suryanarayana and P. Subrahmanyam, The maximal k-full divisor of an integer, Indian J. Pure Appl. Math., Vol. 12, No. 2 (1981), pp. 175-190.
%H A328013 Maurice-Étienne Cloutier, <a href="http://hdl.handle.net/20.500.11794/28374">Les parties k-puissante et k-libre d’un nombre</a>, Thèse de doctorat, Université Laval (2018).
%H A328013 Maurice-Étienne Cloutier, Jean-Marie De Koninck, and Nicolas Doyon, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Cloutier/cloutier2.html">On the powerful and squarefree parts of an integer</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.6.
%H A328013 László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.11, pp. 31-32.
%F A328013 The constant d1 in the paper by Cloutier et al. such that Sum_{k=1..x} A057521(k) = (d1/3)*x^(3/2) + O(x^(4/3)).
%F A328013 Sum_{k=1..x} 1/A055231(k) = d1*x^(1/2) + O(x^(1/3)).
%F A328013 Equals Product_{primes p} (1 + 2/p^(3/2) - 1/p^(5/2)).
%F A328013 Equals (zeta(3/2)/zeta(3)) * Product_{p prime} (1 + (sqrt(p)-1)/(p*(p-sqrt(p)+1))). - _Amiram Eldar_, Dec 26 2024
%e A328013 3.51955505841710664719752940369857817186039808225407...
%t A328013 $MaxExtraPrecision = 500; m = 500; c = LinearRecurrence[{0, 0, -2, 0, 1}, {0, 0, 6, 0, -5}, m]; RealDigits[(1 + 2/2^(3/2) - 1/2^(5/2))*(1 + 2/3^(3/2) - 1/3^(5/2))* Exp[NSum[Indexed[c, n]*(PrimeZetaP[n/2] - 1/2^(n/2) - 1/3^(n/2))/n, {n, 3, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%o A328013 (PARI) prodeulerrat(1 + 2/p^3 - 1/p^5, 1/2) \\ _Amiram Eldar_, Jun 29 2023
%Y A328013 Cf. A055231, A057521, A090699, A191622.
%K A328013 nonn,cons
%O A328013 1,1
%A A328013 _Amiram Eldar_, Oct 01 2019
%E A328013 More terms from _Vaclav Kotesovec_, May 29 2020