A361783 - OEIS

%I #9 Mar 24 2023 11:15:04

%S 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 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 15,20,45,30,1,31,12,20,119,21,3,34,45,8,9,36,25,37,57

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

%H Amiram Eldar, <a href="/A361783/b361783.txt">Table of n, a(n) for n = 1..10000</a>

%H Jozsef Sandor, <a href="https://arxiv.org/abs/1105.0294">On bi-unitary harmonic numbers</a>, arXiv:1105.0294 [math.NT], 2011.

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

%t 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 (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 Cf. A188999, A222266, A286324, A286325 (positions of 1's), A361782 (numerators).

%Y Similar sequences: A099378, A103340, A361317.

%K nonn,frac

%O 1,2

%A _Amiram Eldar_, Mar 24 2023