cp's OEIS Frontend

A381639 Denominators of Sum_{i=1..omega(n)-1} p_{i}/p_{i+1}, where omega(n) = A001221(n) and p_1 < p_2 < ... p_omega(n) are the distinct prime factors of n; a(1) = 1.

%I A381639 #9 Mar 03 2025 13:33:43
%S A381639 1,1,1,1,1,3,1,1,1,5,1,3,1,7,5,1,1,3,1,5,7,11,1,3,1,13,1,7,1,15,1,1,
%T A381639 11,17,7,3,1,19,13,5,1,21,1,11,5,23,1,3,1,5,17,13,1,3,11,7,19,29,1,15,
%U A381639 1,31,7,1,13,33,1,17,23,35,1,3,1,37,5,19,11,39,1
%N A381639 Denominators of Sum_{i=1..omega(n)-1} p_{i}/p_{i+1}, where omega(n) = A001221(n) and p_1 < p_2 < ... p_omega(n) are the distinct prime factors of n; a(1) = 1.
%C A381639 First differs from A119288 at n = 30.
%C A381639 First differs from {A226040(n-1)} at n = 35.
%C A381639 Also denominators of the fractions whose numerators are A381641.
%H A381639 Amiram Eldar, <a href="/A381639/b381639.txt">Table of n, a(n) for n = 1..10000</a>
%H A381639 Paul Erdős and Jean-Louis Nicolas, <a href="https://doi.org/10.1515/9783110852790.169">Grandes valeurs de fonctions liées aux diviseurs premiers consécutifs d'un entier</a>, in: Jean-Marie de Koninck and Claude Levesque (eds.), Théorie des nombres / Number Theory, Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987, De Gruyter, 1989; <a href="https://users.renyi.hu/~p_erdos/1989-08.pdf">alternative link</a>.
%t A381639 a[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, Denominator[Total[Most[p]/Rest[p]]]]; Array[a, 100]
%o A381639 (PARI) a(n) = {my(p = factor(n)[,1]); denominator(sum(i = 1, #p-1, p[i]/p[i+1]));}
%Y A381639 Cf. A001221, A119288, A226040, A381638 (numerators), A381640, A381641.
%K A381639 nonn,easy,frac
%O A381639 1,6
%A A381639 _Amiram Eldar_, Mar 03 2025