OFFSET
1,2
COMMENTS
Sum_{d|n} (1/pod(d)) >= 1 for all n >= 1.
EXAMPLE
Sum_{d|n} (1/pod(d)) for n >= 1: 1, 3/2, 4/3, 13/8, 6/5, 67/36, 8/7, 105/64, 37/27, 171/100, 12/11, 3433/1728, ...
For n=4; Sum_{d|4} (1/pod(d)) = 1/pod(1) + 1/pod(2) + 1/pod(4) = (1/1) + (1/2) + (1/8) = 13/8; a(4) = 13.
MATHEMATICA
Table[Numerator[Sum[Product[1/d , {d, Divisors[k]}], {k, Divisors[n]}]], {n, 1, 50}] (* G. C. Greubel, Mar 04 2019 *)
PROG
(Magma) [Numerator(&+[1 / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..50]]
(PARI) a(n) = numerator(sumdiv(n, d, 1/vecprod(divisors(d)))); \\ Michel Marcus, Mar 03 2019
(Sage) [sum(product(1/j for j in k.divisors()) for k in n.divisors() ).numerator() for n in (1..50)] # G. C. Greubel, Mar 04 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Mar 02 2019
STATUS
approved