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A349502
Numbers k such that the continued fraction of the harmonic mean of the divisors of k contains distinct elements.
3
1, 2, 3, 6, 9, 14, 20, 24, 28, 32, 33, 35, 42, 44, 45, 51, 52, 55, 60, 65, 66, 68, 69, 70, 72, 84, 87, 88, 91, 95, 99, 104, 110, 114, 115, 117, 120, 123, 125, 126, 128, 135, 136, 138, 140, 141, 145, 152, 153, 156, 159, 170, 174, 177, 180, 182, 185, 186, 187, 188
OFFSET
1,2
COMMENTS
All the harmonic numbers (A001599) are terms of this sequence.
LINKS
EXAMPLE
2 is a term since the harmonic mean of the divisors of 2 is 4/3 = 1 + 1/3 and the elements of the continued fraction, {1, 3}, are different.
4 is not a term since the harmonic mean of the divisors of 4 is 12/7 = 1 + 1/(1 + 1/(2 + 1/2)) and the elements of the continued fraction, {1, 1, 2, 2}, are not distinct.
MATHEMATICA
c[n_] := ContinuedFraction[DivisorSigma[0, n]/DivisorSigma[-1, n]]; q[n_] := Length[(cn = c[n])] == Length[DeleteDuplicates[cn]]; Select[Range[200], q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 20 2021
STATUS
approved