A361783 Denominators of the harmonic means of the bi-unitary divisors of the positive integers.

1, 3, 2, 5, 3, 1, 4, 15, 5, 9, 6, 5, 7, 3, 2, 27, 9, 5, 10, 3, 8, 9, 12, 5, 13, 21, 10, 5, 15, 3, 16, 21, 4, 27, 12, 25, 19, 15, 14, 9, 21, 2, 22, 15, 1, 9, 24, 9, 25, 39, 6, 35, 27, 5, 18, 15, 20, 45, 30, 1, 31, 12, 20, 119, 21, 3, 34, 45, 8, 9, 36, 25, 37, 57

Offset: 1

Author

Amiram Eldar, Mar 24 2023

Keywords

• nonn
• frac

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jozsef Sandor, On bi-unitary harmonic numbers, arXiv:1105.0294 [math.NT], 2011.

Crossrefs

Cf. A188999, A222266, A286324, A286325 (positions of 1's), A361782 (numerators).

Similar sequences: A099378, A103340, A361317.

Programs

Mathematica

f[p_, e_] := p^e * If[OddQ[e], (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2))]; a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]

PARI

a(n) = {my(f = factor(n), p, e); denominator(n * prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2];  if(e%2, (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2))))); }

Formula

a(n) = denominator(n*A286324(n)/A188999(n)).