cp's OEIS Frontend

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

%I A361783 #9 Mar 24 2023 11:15:04
%S A361783 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,
%T A361783 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,
%U A361783 15,20,45,30,1,31,12,20,119,21,3,34,45,8,9,36,25,37,57
%N A361783 Denominators of the harmonic means of the bi-unitary divisors of the positive integers.
%H A361783 Amiram Eldar, <a href="/A361783/b361783.txt">Table of n, a(n) for n = 1..10000</a>
%H A361783 Jozsef Sandor, <a href="https://arxiv.org/abs/1105.0294">On bi-unitary harmonic numbers</a>, arXiv:1105.0294 [math.NT], 2011.
%F A361783 a(n) = denominator(n*A286324(n)/A188999(n)).
%t A361783 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]
%o A361783 (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))))); }
%Y A361783 Cf. A188999, A222266, A286324, A286325 (positions of 1's), A361782 (numerators).
%Y A361783 Similar sequences: A099378, A103340, A361317.
%K A361783 nonn,frac
%O A361783 1,2
%A A361783 _Amiram Eldar_, Mar 24 2023