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 A308041 #17 Dec 24 2024 07:31:04
%S A308041 7,6,8,7,1,8,3,6,2,4,4,6,4,8,5,1,9,8,6,7,2,7,3,4,3,3,2,4,5,5,3,5,0,5,
%T A308041 2,5,2,3,4,2,5,5,7,4,0,4,1,1,9,0,4,1,1,0,7,0,1,5,4,1,3,5,2,9,3,4,8,6,
%U A308041 0,7,7,6,8,3,3,7,9,0,8,0,3,9,3,3,2,8,8,0,7,6,4,8,9,6,9,1,4,7,5,9,5,3,3,7,2,4
%N A308041 Decimal expansion of lim_{m->oo} (1/log(m))*Sum_{k=1..m} 1/usigma(k), where usigma(k) is the sum of unitary divisors of k (A034448).
%H A308041 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 51 (constant Y3).
%H A308041 V. Sita Ramaiah and D. Suryanarayana, <a href="https://web.archive.org/web/20200803214209/http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005bab_1334.pdf">Sums of reciprocals of some multiplicative functions - II</a>, Indian J. Pure Appl. Math., Vol. 11 (1980), pp. 1334-1355 (eq. 3.8-3.9, p. 1352-1353).
%H A308041 László Tóth, <a href="http://emis.ams.org/journals/JIS/VOL20/Toth/toth25.html">Alternating sums concerning multiplicative arithmetic functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1 (section 4.9, p. 29).
%F A308041 From _Amiram Eldar_, Dec 23 2024: (Start)
%F A308041 Equals Product_{p prime} ((1-1/p) * (1 + Sum_{k>=1} 1/(p^k+1))).
%F A308041 Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A063974(k). (End)
%e A308041 0.76871836244648519867273433245535052523425574041190...
%t A308041 $MaxExtraPrecision = 1000; m = 1000; f[p_] := 1 - (p - 1)/p*Sum[1/p^k/(p^k + 1), {k, 1, m}]; c = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x]*Range[0, m]];RealDigits[f[2]*Exp[NSum[Indexed[c, k]*(PrimeZetaP[k] - 1/2^k)/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%Y A308041 Cf. A034448, A063974, A308039 (corresponding limit with sigma).
%K A308041 nonn,cons
%O A308041 0,1
%A A308041 _Amiram Eldar_, May 10 2019
%E A308041 More digits from _Vaclav Kotesovec_, Jun 13 2021