A361784 Harmonic means the bi-unitary divisors of the bi-unitary harmonic numbers (A286325).

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, 25, 24, 19, 25, 23, 27, 33, 31, 44, 32, 34, 30, 25, 36, 13, 46, 31, 21, 29, 40, 38, 33, 28, 40, 48, 38, 29, 45, 34, 47, 28, 32, 32, 44, 60, 27, 32, 28, 46, 26, 51

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..313

Jozsef Sandor, On bi-unitary harmonic numbers, arXiv:1105.0294 [math.NT], 2011.

Formula

a(n) = A361782(A286325(n)).

Example

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.

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

Prog

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

Crossrefs

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

Similar sequences: A001600, A006087, A361318.

Sequence in context: A089266 A178993 A193768 * A361318 A205791 A039696

Adjacent sequences: A361781 A361782 A361783 * A361785 A361786 A361787

Keyword

nonn

Author

Amiram Eldar, Mar 24 2023

Status

approved