cp's OEIS Frontend

A386926 a(n) = denominator(Sum_{k=1..n} d(k+1)/d(k)), where d is the number of divisors function.

%I A386926 #7 Aug 09 2025 07:45:24
%S A386926 1,1,2,6,6,3,3,12,4,4,4,12,12,12,6,30,30,30,30,30,30,15,15,120,120,
%T A386926 120,120,40,40,40,40,120,120,120,120,360,360,360,360,360,360,360,360,
%U A386926 360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360
%N A386926 a(n) = denominator(Sum_{k=1..n} d(k+1)/d(k)), where d is the number of divisors function.
%H A386926 Amiram Eldar, <a href="/A386926/b386926.txt">Table of n, a(n) for n = 1..10000</a>
%H A386926 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.
%e A386926 Fractions begin with 2, 3, 9/2, 31/6, 43/6, 23/3, 29/3, 125/12, 47/4, 49/4, 61/4, ...
%t A386926 With[{s = DivisorSigma[0, Range[100]]}, Denominator[Accumulate[Rest[s]/Most[s]]]]
%o A386926 (PARI) list(nmax) = {my(s = 0, d1 = 1, d2); for(n = 2, nmax, d2 = numdiv(n); s += (d2/d1); print1(denominator(s), ", "); d1 = d2);}
%Y A386926 Cf. A000005, A386925 (numerators).
%K A386926 nonn,frac,easy
%O A386926 1,3
%A A386926 _Amiram Eldar_, Aug 08 2025