login
A361783
Denominators of the harmonic means of the bi-unitary divisors of the positive integers.
5
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
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
KEYWORD
nonn,frac
AUTHOR
Amiram Eldar, Mar 24 2023
STATUS
approved