|
%I #27 Feb 18 2024 02:04:57
%S 0,1,1,1,1,5,1,1,1,7,1,5,1,9,8,1,1,5,1,7,10,13,1,5,1,15,1,9,1,31,1,1,
%T 14,19,12,5,1,21,16,7,1,41,1,13,8,25,1,5,1,7,20,15,1,5,16,9,22,31,1,
%U 31,1,33,10,1,18,61,1,19,26,59,1,5,1,39,8,21,18,71,1,7,1,43,1,41,22,45,32
%N If n = Product (p_j^k_j), a(n) = numerator of Sum 1/p_j (the denominator of this sum is A007947).
%C For n=1, the empty sum = 0 = 0/1 = a(1)/A007947(1), thus a(1) should be 0. - _Antti Karttunen_, Mar 04 2018
%H Antti Karttunen, <a href="/A028235/b028235.txt">Table of n, a(n) for n = 1..65537</a>
%F Fraction is additive with a(p^e) = 1/p.
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A007947(k) = Sum_{p prime} 1/p^2 = 0.452247... (A085548). - _Amiram Eldar_, Sep 29 2023
%e Fractions begin with 0, 1/2, 1/3, 1/2, 1/5, 5/6, 1/7, 1/2, 1/3, 7/10, 1/11, 5/6, ...
%t a[1] = 0; a[n_] := 1/FactorInteger[n][[All, 1]] // Total // Numerator;
%t Array[a, 100] (* _Jean-François Alcover_, May 08 2019 *)
%o (PARI) A028235(n) = numerator(vecsum(apply(p->(1/p), factor(n)[, 1]))); \\ _Antti Karttunen_, Mar 04 2018
%Y Cf. A007947 (denominators), A085548.
%K nonn,frac,easy
%O 1,6
%A _N. J. A. Sloane_.
%E More terms from _Erich Friedman_.
%E Term a(1) changed to 0 by _Antti Karttunen_, Mar 04 2018
|
