OFFSET
1,2
COMMENTS
Sum_{d|n} (pod(d)/tau(d)) > 1 for all n > 1.
FORMULA
a(p) = p + 2 for p = odd primes.
EXAMPLE
Sum_{d|n} (pod(d)/tau(d)) for n >= 1: 1, 2, 5/2, 14/3, 7/2, 25/2, 9/2, 62/3, 23/2, 59/2, ...
For n=4; Sum_{d|4} (pod(d)/tau(d)) = pod(1)/tau(1) + pod(2)/tau(2) + pod(4)/tau(4) = 1/1 + 2/2 + 8/3 = 14/3; a(4) = 14.
MATHEMATICA
Array[Numerator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[0, #] &] &, 49] (* Michael De Vlieger, Mar 24 2019 *)
PROG
(Magma) [Numerator(&+[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, vecprod(divisors(d))/numdiv(d))); \\ Michel Marcus, Mar 23 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 22 2019
STATUS
approved