A099378 Denominators of the harmonic means of the divisors of the positive integers.

1, 3, 2, 7, 3, 1, 4, 15, 13, 9, 6, 7, 7, 3, 2, 31, 9, 13, 10, 7, 8, 9, 12, 5, 31, 21, 10, 1, 15, 3, 16, 21, 4, 27, 12, 91, 19, 15, 14, 9, 21, 2, 22, 7, 13, 9, 24, 31, 19, 31, 6, 49, 27, 5, 18, 15, 20, 45, 30, 7, 31, 12, 52, 127, 21, 3, 34, 21, 8, 9, 36, 65, 37, 57, 62, 35, 24, 7, 40, 93

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Ore's Conjecture

Example

1, 4/3, 3/2, 12/7, 5/3, 2, 7/4, 32/15, ...

Mathematica

f[n_] := DivisorSigma[0, n]/Plus @@ (1/Divisors@n); Denominator@ Array[f, 80] (* Robert G. Wilson v, Aug 04 2010 *)
Table[Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]], {n, 80}] (* Ivan Neretin, Nov 13 2016 *)

Prog

(PARI) a(n) = my(d=divisors(n)); denominator(#d/sum(k=1, #d, 1/d[k])); \\ Michel Marcus, Nov 13 2016
(PARI) first(n)=my(v=vector(n)); forfactored(k=1, n, v[k[1]]=denominator(sigma(k, 0)/sigma(k, -1))); v \\ Charles R Greathouse IV, Nov 01 2021
(Python)
from sympy import gcd, divisor_sigma
def A099378(n): return (lambda x, y: x//gcd(x, y*n))(divisor_sigma(n), divisor_sigma(n, 0)) # Chai Wah Wu, Oct 20 2021

Crossrefs

Cf. A099377.

Sequence in context: A245601 A355934 A296513 * A182885 A182891 A071190

Adjacent sequences: A099375 A099376 A099377 * A099379 A099380 A099381

Keyword

nonn,frac

Author

Eric W. Weisstein, Oct 13 2004

Extensions

More terms from Robert G. Wilson v, Aug 04 2010

Status

approved