OFFSET
1,3
FORMULA
a(n) is the numerator of (sum(i = 1 .. n, Omega(i)))/n, where Omega is the number of prime factors function (counted with multiplicity, see A001222).
EXAMPLE
a(8) = 11, since the integers from 1 to 8 have between them a total of 11 prime factors, making our fraction here 11/8.
a(9) = 13, since the integers from 1 to 9 have between them a total of 13 prime factors, making our fraction here 13/9.
a(10) = 3, since the integers from 1 to 10 have between them a total of 15 prime factors, making our fraction here 15/10 = 3/2.
MAPLE
N:= 100: # to get terms a(1) to a(N)
map(numer, zip(`/`, ListTools:-PartialSums([seq(numtheory:-bigomega(n), n=1..N)]), [$1..N])); # Robert Israel, Aug 29 2014
MATHEMATICA
Numerator[Array[Plus@@Last/@FactorInteger[#!] &, 120, 2]/Range[2, 121]]
PROG
(PARI) lista(nn) = {s = 0; for (n=1, nn, s += bigomega(n); print1(numerator(s/n), ", "); ); } \\ Michel Marcus, Aug 28 2014
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Alonso del Arte, Aug 22 2014
STATUS
approved