OFFSET
1,2
COMMENTS
Sum_{d|n} (d/pod(d)) >= 1 for all n >= 1.
Sum_{d|n} (d/pod(d)) = 2 iff n = primes (A000040).
FORMULA
a(p) = 2 for p = primes.
EXAMPLE
Sum_{d|n} (d/pod(d)) for n >= 1: 1, 2, 2, 5/2, 2, 19/6, 2, 21/8, 7/3, 31/10, 2, 529/144, 2, 43/14, 46/15, 169/64, ...
For n=4; Sum_{d|4} (d/pod(d)) = 1/pod(1) + 2/pod(2) + 4/pod(4) = 1/1 + 2/2 + 4/8 = 5/2; a(4) = 5.
MATHEMATICA
Table[Numerator[Sum[k/Product[j, {j, Divisors[k]}], {k, Divisors[n]}]], {n, 1, 60}] (* G. C. Greubel, Mar 04 2019 *)
PROG
(Magma) [Numerator(&+[d / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
(Sage) [sum(k/product(j for j in k.divisors()) for k in n.divisors()).numerator() for n in (1..60)] # G. C. Greubel, Mar 04 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 03 2019
STATUS
approved