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 A386925 #7 Aug 09 2025 07:47:47
%S A386925 2,3,9,31,43,23,29,125,47,49,61,187,211,223,119,607,697,707,797,817,
%T A386925 847,431,491,3973,4133,4253,4433,1491,1651,1661,1781,5423,5543,5663,
%U A386925 5933,17879,18599,18959,19679,19769,21209,21299,22379,22739,22979,23159,24959,25067
%N A386925 a(n) = numerator(Sum_{k=1..n} d(k+1)/d(k)), where d is the number of divisors function.
%H A386925 Amiram Eldar, <a href="/A386925/b386925.txt">Table of n, a(n) for n = 1..10000</a>
%H A386925 Florian Luca and Igor E. Shparlinski, <a href="https://doi.org/10.1007/s00605-007-0511-3">On the values of the divisor function</a>, Monatshefte für Mathematik, Vol. 154, No. 1 (2008), pp. 59-69.
%F A386925 a(n)/A386926(n) ≍ n * sqrt(log(n)) (Luca and Shparlinski, 2008).
%e A386925 Fractions begin with 2, 3, 9/2, 31/6, 43/6, 23/3, 29/3, 125/12, 47/4, 49/4, 61/4, ...
%t A386925 With[{s = DivisorSigma[0, Range[100]]}, Numerator[Accumulate[Rest[s]/Most[s]]]]
%o A386925 (PARI) list(nmax) = {my(s = 0, d1 = 1, d2); for(n = 2, nmax, d2 = numdiv(n); s += (d2/d1); print1(numerator(s), ", "); d1 = d2);}
%Y A386925 Cf. A000005, A386926 (denominators).
%K A386925 nonn,frac,easy
%O A386925 1,1
%A A386925 _Amiram Eldar_, Aug 08 2025