OFFSET
1,2
COMMENTS
If n is prime, a(n) = n.
a(n) is a divisor of n. How often is it < n? - Chai Wah Wu, Oct 02 2017
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
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) = denominator(175/6) = 6.
MAPLE
a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:
seq(denom(a(n)), n = 1 .. 100);
MATHEMATICA
Table[Denominator@ Sum[DivisorSigma[1, n/d]^d/d, {d, Divisors@ n}], {n, 69}] (* Michael De Vlieger, Feb 19 2016 *)
PROG
(PARI) a(n) = denominator(sumdiv(n, d, sigma(n/d)^d/d)); \\ Michel Marcus, Feb 17 2016
(Python)
from __future__ import division
from sympy import divisors, divisor_sigma, gcd
def A268982(n):
return n//gcd(n, sum(d*divisor_sigma(d)**(n//d) for d in divisors(n, generator=True))) # Chai Wah Wu, Oct 02 2017
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Gevorg Hmayakyan, Feb 16 2016
STATUS
approved