OFFSET
1,2
COMMENTS
Sum_{d|n} sigma(d)/pod(d) > 1 for all n > 1.
FORMULA
a(p) = 2p+1 for p = primes (A000040).
EXAMPLE
For n=4; Sum_{d|4} sigma(d)/pod(d) = sigma(1)/pod(1) + sigma(2)/pod(2) + sigma(4)/pod(4) = 1/1 + 3/2 + 7/8 = 27/8; a(4) = 27.
MATHEMATICA
Array[Numerator@ DivisorSum[#, Total[#]/(Times @@ #) &@ Divisors@ # &] &, 48] (* Michael De Vlieger, Feb 24 2019 *)
PROG
(Magma) [Numerator(&+[SumOfDivisors(d) / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, sigma(d)/vecprod(divisors(d)))); \\ Michel Marcus, Feb 23 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Feb 23 2019
STATUS
approved