A386925 a(n) = numerator(Sum_{k=1..n} d(k+1)/d(k)), where d is the number of divisors function.

2, 3, 9, 31, 43, 23, 29, 125, 47, 49, 61, 187, 211, 223, 119, 607, 697, 707, 797, 817, 847, 431, 491, 3973, 4133, 4253, 4433, 1491, 1651, 1661, 1781, 5423, 5543, 5663, 5933, 17879, 18599, 18959, 19679, 19769, 21209, 21299, 22379, 22739, 22979, 23159, 24959, 25067

Offset

1,1

Links

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

Florian Luca and Igor E. Shparlinski, On the values of the divisor function, Monatshefte für Mathematik, Vol. 154, No. 1 (2008), pp. 59-69.

Formula

a(n)/A386926(n) ≍ n * sqrt(log(n)) (Luca and Shparlinski, 2008).

Example

Fractions begin with 2, 3, 9/2, 31/6, 43/6, 23/3, 29/3, 125/12, 47/4, 49/4, 61/4, ...

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A386926 (denominators).

Sequence in context: A073950 A281270 A322752 * A277345 A259943 A296263

Adjacent sequences: A386922 A386923 A386924 * A386926 A386927 A386928

Keyword

nonn,frac,easy

Author

Amiram Eldar, Aug 08 2025

Status

approved