A386924 a(n) = denominator(Sum_{k=1..n} d(k)/d(k+1)), where d is the number of divisors function.

2, 2, 6, 3, 6, 6, 3, 1, 4, 4, 12, 12, 12, 12, 60, 60, 60, 60, 20, 20, 20, 20, 10, 30, 60, 60, 60, 60, 30, 30, 30, 15, 15, 15, 45, 90, 45, 45, 90, 90, 180, 180, 180, 180, 180, 180, 36, 36, 36, 36, 36, 36, 18, 18, 9, 9, 9, 9, 18, 18, 9, 9, 63, 252, 252, 252, 252

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Maxim A. Korolev, On Karatsuba's problem concerning the divisor function, Monatshefte für Mathematik, Vol. 168, No. 3 (2012), pp. 403-441; arXiv preprint, arXiv:1011.1391 [math.NT], 2010.

Example

Fractions begin with 1/2, 3/2, 13/6, 11/3, 25/6, 37/6, 20/3, 8, 35/4, 43/4, 133/12, ...

Mathematica

With[{s = DivisorSigma[0, Range[100]]}, Denominator[Accumulate[Most[s]/Rest[s]]]]

Prog

(PARI) list(nmax) = {my(s = 0, d1 = 1, d2); for(n = 2, nmax, d2 = numdiv(n); s += (d1/d2); print1(denominator(s), ", "); d1 = d2); }

Crossrefs

Cf. A000005, A386923 (numerators).

Sequence in context: A085738 A227608 A276484 * A100641 A028421 A263003

Adjacent sequences: A386921 A386922 A386923 * A386925 A386926 A386927

Keyword

nonn,frac,easy

Author

Amiram Eldar, Aug 08 2025

Status

approved