A361784 - OEIS

%I #9 Mar 24 2023 11:15:14

%S 1,2,3,4,4,6,7,7,8,11,13,13,12,10,16,7,18,16,15,24,15,20,20,18,14,22,

%T 25,24,19,25,23,27,33,31,44,32,34,30,25,36,13,46,31,21,29,40,38,33,28,

%U 40,48,38,29,45,34,47,28,32,32,44,60,27,32,28,46,26,51

%N Harmonic means the bi-unitary divisors of the bi-unitary harmonic numbers (A286325).

%H Amiram Eldar, <a href="/A361784/b361784.txt">Table of n, a(n) for n = 1..313</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) = A361782(A286325(n)).

%e a(3) = 3 since A286325(3) = 45, the bi-unitary divisors of 45 are 1, 5, 9, and 45, and their harmonic mean is 3.

%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))]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 10^5], IntegerQ]

%o (PARI) bhmean(n) = {my(f = factor(n), p, e); 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)))); }

%o lista(kmax) = {my(bh); for(k = 1, kmax, bh = bhmean(k); if(denominator(bh) == 1, print1(bh, ", "))); }

%Y Cf. A188999, A286324, A286325, A361782, A361783.

%Y Similar sequences: A001600, A006087, A361318.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 24 2023