OFFSET
1,2
COMMENTS
If n is prime, a(n) = n^2 + n + 1. - Robert Israel, Feb 16 2016
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..4191
EXAMPLE
sigma(1)^6/6 + sigma(2)^3/3 + sigma(3)^2/2 + sigma(6)^1/1 = 1/6 + 9 + 8 + 12 = 175/6. a(6) = numerator(175/6) = 175.
MAPLE
a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:
seq(numer(a(n)), n = 1 .. 100);
MATHEMATICA
Table[Numerator@ Sum[DivisorSigma[1, n/d]^d/d, {d, Divisors@ n}], {n,
38}] (* Michael De Vlieger, Feb 19 2016 *)
PROG
(PARI) a(n) = numerator(sumdiv(n, d, sigma(n/d)^d/d)); \\ Michel Marcus, Feb 19 2016
(Python)
from __future__ import division
from sympy import divisors, divisor_sigma, gcd
def A267310(n):
m = sum(d*divisor_sigma(d)**(n//d) for d in divisors(n, generator=True))
return m//gcd(m, n) # Chai Wah Wu, Oct 02 2017
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Gevorg Hmayakyan, Feb 16 2016
STATUS
approved