

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
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OFFSET

1,2


LINKS



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



KEYWORD

nonn,frac


AUTHOR



EXTENSIONS



STATUS

approved



