OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
Fractions begin: 1, 3/2, 3/2, 2, 3/2, 9/4, 3/2, 5/2, 2, 9/4, ...
For n = 2, n has 2 divisors, 1 and 2. Their numbers of divisors are tau(1) = 1 and tau(2) = 2, and their mean number of divisors is (1 + 2)/2 = 3/2. Therefore a(2) = numerator(3/2) = 3.
MATHEMATICA
f[p_, e_] := (e + 2)/2; a[1] = 1; a[n_] := Numerator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]
PROG
(PARI) a(n) = numerator(vecprod(apply(x -> x/2 +1, factor(n)[, 2])));
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Jul 23 2024
STATUS
approved