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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
1, 2, 20, 52, 156, 768, 8244, 25808, 406764, 3610688, 41395016, 453695175, 3325792768
OFFSET
1,2
EXAMPLE
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
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]
CROSSREFS
Sequence in context: A202602 A097652 A261838 * A225065 A059211 A331090
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Nov 20 2021
STATUS
approved