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A349473
Irregular triangle read by rows: the n-th row contains the elements in the continued fraction of the harmonic mean of the divisors of n.
12
1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 2, 7, 2, 2, 13, 2, 4, 2, 1, 1, 5, 2, 1, 1, 3, 1, 1, 6, 2, 3, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 8, 2, 1, 3, 3, 1, 1, 9, 2, 1, 6, 2, 1, 1, 1, 2, 2, 2, 4, 1, 1, 11, 3, 5, 2, 2, 2, 1, 1, 2, 2, 2, 10, 2, 1, 2, 3, 3, 1, 1, 14
OFFSET
1,3
COMMENTS
For an odd prime p > 3, the p-th row has a length 3 with a(p, 1) = a(p, 2) = 1 and a(p, 3) = (p-1)/2.
For a harmonic number m = A001599(k), the m-th row has a length 1 with a(k, 1) = A099377(m) = A001600(k).
EXAMPLE
The first ten rows of the triangle are:
1,
1, 3,
1, 2,
1, 1, 2, 2,
1, 1, 2,
2,
1, 1, 3,
2, 7, 2,
2, 13,
2, 4, 2
...
MATHEMATICA
row[n_] := ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; Table[row[k], {k, 1, 29}] // Flatten
CROSSREFS
Cf. A349474 (row lengths).
Sequence in context: A016569 A072801 A098872 * A167366 A139436 A212305
KEYWORD
nonn,tabf
AUTHOR
Amiram Eldar, Nov 19 2021
STATUS
approved