OFFSET
1,6
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..10000
FORMULA
Fraction is additive with a(p^e) = 1/p^e.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/k = Sum_{p prime} 1/(p*(p+1)) = 0.330229... (A179119). - Amiram Eldar, Sep 29 2023
EXAMPLE
Fractions begin with 1, 1/2, 1/3, 1/4, 1/5, 5/6, 1/7, 1/8, 1/9, 7/10, 1/11, 7/12, ...
MATHEMATICA
a[n_] := n * Total[1/Power @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Sep 29 2023 *)
PROG
(Magma) a028236:=func< k | k eq 1 select 1 else Numerator(&+[ f[i, 1]^-f[i, 2]: i in [1..#f] ]) where f is Factorization(k) >; [ a028236(n):n in [1..82] ]; // Klaus Brockhaus, Nov 06 2010
(Haskell)
a028236 n = sum $ map (div n) $ a141809_row n
-- Reinhard Zumkeller, Nov 10 2013
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
EXTENSIONS
More terms from Erich Friedman
STATUS
approved