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 A327574 #8 Jun 13 2020 07:58:14
%S A327574 7,3,0,7,1,8,2,4,2,1,2,7,3,8,4,2,2,5,8,3,8,9,7,5,4,6,8,1,7,3,5,3,0,1,
%T A327574 6,1,9,5,7,2,5,6,4,3,3,8,6,1,7,2,7,8,6,9,7,0,7,3,3,6,7,6,2,3,0,1,0,7,
%U A327574 9,8,8,3,3,2,8,0,0,5,3,4,6,3,7,0,2,9,9
%N A327574 Decimal expansion of the constant that appears in the asymptotic formula for average order of the infinitary divisors sum function (A049417).
%C A327574 The asymptotic mean of the infinitary abundancy index lim_{n->oo} (1/n) * Sum_{k=1..n} A049417(k)/k = 1.461436... is twice this constant. - _Amiram Eldar_, Jun 13 2020
%D A327574 Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7.5, pp. 53-54.
%H A327574 Graeme L. Cohen and Peter Hagis, Jr., <a href="http://dx.doi.org/10.1155/S0161171293000456">Arithmetic functions associated with infinitary divisors of an integer</a>, International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (1993), pp. 373-383.
%F A327574 Equals Limit_{k->oo} A327566(k)/k^2.
%F A327574 Equals (1/2) * Product_{P} (1 + 1/(P*(P+1))), where P are numbers of the form p^(2^k) where p is prime and k >= 0 (A050376).
%e A327574 0.730718242127384225838975468173530161957256433861727...
%t A327574 $MaxExtraPrecision = 1000; m = 1000; em = 10; f[x_] := Sum[Log[1 + x^(2^e)/(1 + 1/x^(2^e))], {e, 0, em}]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[(1/2) * Exp[NSum[Indexed[c, k]*PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%Y A327574 Cf. A049417, A050376, A327566.
%Y A327574 Cf. A013661 (corresponding constant for all divisors), A275480 (exponential), A306633 (unitary), A307160 (bi-unitary).
%K A327574 nonn,cons
%O A327574 0,1
%A A327574 _Amiram Eldar_, Sep 17 2019