OFFSET
1,2
COMMENTS
Sum_{d|n} (tau(d)/sigma(d)) >= 1 for all n >= 1.
FORMULA
a(p) = (p+3) / gcd(p+3, p+1) for p = primes p.
EXAMPLE
For n=4; Sum_{d|4} (tau(d)/sigma(d)) = (tau(1)/sigma(1))+(tau(2)/sigma(2))+(tau(4)/sigma(4)) = (1/1)+(2/3)+(3/7) = 44/21; a(4) = 44.
MATHEMATICA
Array[Numerator@ DivisorSum[#, Divide @@ DivisorSigma[{0, 1}, #] &] &, 63] (* Michael De Vlieger, Feb 15 2019 *)
PROG
(Magma) [Numerator(&+[NumberOfDivisors(d) / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, numdiv(d)/sigma(d))); \\ Michel Marcus, Feb 13 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Jan 27 2019
STATUS
approved