A349503 a(n) is the least number k such that the continued fraction of the harmonic mean of the divisors of k contains n elements that are all distinct.

1, 2, 20, 52, 156, 768, 8244, 25808, 406764, 3610688, 41395016, 453695175, 3325792768

Offset: 1

Author

Amiram Eldar, Nov 20 2021

Keywords

• nonn
• more

Examples

			The elements of the continued fractions of the harmonic mean of the divisors of the first 13 terms:
   n        a(n)  elements
  --  ----------  -----------------------------
   1           1  1
   2           2  1,3
   3          20  2,1,6
   4          52  3,5,2,4
   5         156  4,1,3,2,5
   6         768  6,1,3,4,2,13
   7        8244  7,11,8,3,1,13,2
   8       25808  5,6,3,13,1,2,4,7
   9      406764  7,8,3,6,9,2,1,4,12
  10     3610688  7,18,5,2,3,6,1,4,13,11
  11    41395016  7,1,12,8,4,2,3,5,19,6,10
  12   453695175  16,5,8,1,10,48,7,13,2,3,6,4
  13  3325792768  19,1,21,7,6,3,12,13,5,9,2,8,4
		

Crossrefs

Cf. A349473, A349502.

Programs

Mathematica

cflen[n_] := Module[{cf = ContinuedFraction[DivisorSigma[0, n]/DivisorSigma[-1, n]], len}, If[(len = Length[cf]) == Length[DeleteDuplicates[cf]], len, 0]]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = cflen[n]; If[i > 0 && i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; TakeWhile[s, # > 0 &]]; seq[10, 10^7]