A099377 Numerators of the harmonic means of the divisors of the positive integers.

1, 4, 3, 12, 5, 2, 7, 32, 27, 20, 11, 18, 13, 7, 5, 80, 17, 36, 19, 20, 21, 22, 23, 16, 75, 52, 27, 3, 29, 10, 31, 64, 11, 68, 35, 324, 37, 38, 39, 32, 41, 7, 43, 22, 45, 23, 47, 120, 49, 100, 17, 156, 53, 18, 55, 56, 57, 116, 59, 30, 61, 31, 189, 448, 65, 11, 67, 68, 23, 35

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); Numerator@ Array[f, 70] (* Robert G. Wilson v, Aug 04 2010 *)
Table[Numerator[DivisorSigma[0, n]/DivisorSigma[-1, n]], {n, 70}] (* Ivan Neretin, Nov 13 2016 *)

Prog

(PARI) a(n) = my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); \\ Michel Marcus, Nov 13 2016
(Python)
from sympy import gcd, divisor_sigma
def A099377(n): return (lambda x, y: y*n//gcd(x, y*n))(divisor_sigma(n), divisor_sigma(n, 0)) # Chai Wah Wu, Oct 20 2021

Crossrefs

Cf. A099378.

Sequence in context: A271888 A271098 A269718 * A121844 A091512 A106285

Adjacent sequences: A099374 A099375 A099376 * A099378 A099379 A099380

Keyword

nonn,frac

Author

Eric W. Weisstein, Oct 13 2004

Extensions

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

Status

approved