%I #25 Sep 29 2023 04:04:20
%S 1,1,1,1,1,5,1,1,1,7,1,7,1,9,8,1,1,11,1,9,10,13,1,11,1,15,1,11,1,31,1,
%T 1,14,19,12,13,1,21,16,13,1,41,1,15,14,25,1,19,1,27,20,17,1,29,16,15,
%U 22,31,1,47,1,33,16,1,18,61,1,21,26,59,1,17,1,39,28,23,18,71,1,21,1,43
%N If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j^k_j.
%H Klaus Brockhaus, <a href="/A028236/b028236.txt">Table of n, a(n) for n = 1..10000</a>
%F Fraction is additive with a(p^e) = 1/p^e.
%F a(n) = Sum_{k=1..A001221(n)} n/A141809(n,k). - _Reinhard Zumkeller_, Nov 10 2013
%F 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
%e 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, ...
%t a[n_] := n * Total[1/Power @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Sep 29 2023 *)
%o (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
%o (Haskell)
%o a028236 n = sum $ map (div n) $ a141809_row n
%o -- _Reinhard Zumkeller_, Nov 10 2013
%Y Denominator is n (A000027).
%Y Cf. A001221, A141809, A179119.
%K nonn,easy,frac
%O 1,6
%A _N. J. A. Sloane_
%E More terms from _Erich Friedman_