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A099378 Denominators of the harmonic means of the divisors of the positive integers. 46
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 (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); 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
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 26 07:52 EDT 2024. Contains 372807 sequences. (Running on oeis4.)