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A099377 Numerators of the harmonic means of the divisors of the positive integers. 49
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Oct 13 2004
EXTENSIONS
More terms from Robert G. Wilson v, Aug 04 2010
STATUS
approved

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Last modified May 28 00:20 EDT 2024. Contains 372900 sequences. (Running on oeis4.)