OFFSET
1,2
COMMENTS
Sum_{d|n} (d/tau(d)) >= 1 for all n >= 1.
FORMULA
a(p) = p + 2 for p = odd primes.
EXAMPLE
Sum_{d|n} (d/tau(d)) for n >= 1: 1, 2, 5/2, 10/3, 7/2, 5, 9/2, 16/3, 11/2, 7, 13/2, 25/3, 15/2, 9, 35/4, 128/15, ...
For n=4; Sum_{d|4} (d/tau(d)) = 1/tau(1) + 2/tau(2) + 4/tau(4) = 1/1 + 2/2 + 4/3 = 10/3; a(4) = 10.
MATHEMATICA
Table[Numerator[Sum[k/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 80}] (* G. C. Greubel, Mar 04 2019 *)
PROG
(Magma) [Numerator(&+[d / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = numerator(sumdiv(n, d, d/numdiv(d))); \\ Michel Marcus, Mar 03 2019
(Sage) [sum(k/sigma(k, 0) for k in n.divisors()).numerator() for n in (1..80)] # G. C. Greubel, Mar 04 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 03 2019
STATUS
approved