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 A336065 #9 Jul 08 2020 05:08:49 %S A336065 8,4,8,9,5,7,1,9,5,0,0,4,4,9,3,3,2,8,1,4,2,7,1,0,9,7,6,8,5,4,4,3,5,2, %T A336065 9,2,6,7,7,9,1,4,7,2,8,9,9,4,9,1,8,1,0,0,9,7,8,8,1,7,6,4,4,2,0,5,6,1, %U A336065 5,7,0,9,6,6,9,2,4,6,7,0,3,0,0,1,5,8,6 %N A336065 Decimal expansion of the asymptotic density of the numbers divisible by the maximal exponent in their prime factorization (A336064). %D A336065 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, chapter 3, p. 331. %H A336065 Andrzej Schinzel and Tibor Šalát, <a href="https://dml.cz/handle/10338.dmlcz/136624">Remarks on maximum and minimum exponents in factoring</a>, Mathematica Slovaca, Vol. 44, No. 5 (1994), pp. 505-514. %F A336065 Equals 1/zeta(2) + Sum_{k>=2} ((1/zeta(k+1)) * Product_{p prime, p|k} ((p^(k-e(p,k)+1) - 1)/(p^(k+1) - 1)) - (1/zeta(k)) * Product_{p prime, p|k} ((p^(k-e(p,k)) - 1)/(p^k - 1))), where e(p,k) is the largest exponent of p dividing k. %e A336065 0.848957195004493328142710976854435292677914728994918... %t A336065 f[k_] := Module[{f = FactorInteger[k]}, p = f[[;; , 1]]; e = f[[;; , 2]]; (1/Zeta[k + 1])* Times @@ ((p^(k - e + 1) - 1)/(p^(k + 1) - 1)) - (1/Zeta[k]) * Times @@ ((p^(k - e) - 1)/(p^k - 1))]; RealDigits[1/Zeta[2] + Sum[f[k], {k, 2, 1000}], 10, 100][[1]] %Y A336065 Cf. A051903, A059956, A336064. %K A336065 nonn,cons %O A336065 0,1 %A A336065 _Amiram Eldar_, Jul 07 2020