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

1,2

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.

Formula

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

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]

Prog

(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))))); }

Crossrefs

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

Similar sequences: A099378, A103340, A361317.

Sequence in context: A103340 A106615 A361317 * A194736 A333363 A130299

Adjacent sequences: A361780 A361781 A361782 * A361784 A361785 A361786

Keyword

nonn,frac

Author

Amiram Eldar, Mar 24 2023

Status

approved