A381641 Numerators of Sum_{i=1..omega(n)-1} (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) = 0.
0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 5, 2, 0, 0, 1, 0, 3, 4, 9, 0, 1, 0, 11, 0, 5, 0, 11, 0, 0, 8, 15, 2, 1, 0, 17, 10, 3, 0, 19, 0, 9, 2, 21, 0, 1, 0, 3, 14, 11, 0, 1, 6, 5, 16, 27, 0, 11, 0, 29, 4, 0, 8, 35, 0, 15, 20, 31, 0, 1, 0, 35, 2, 17, 4, 43, 0, 3, 0
Offset: 1
Examples
Fractions begin with 0, 0, 0, 0, 0, 1/3, 0, 0, 0, 3/5, 0, 1/3, ...
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Paul Erdős and Jean-Louis Nicolas, Grandes valeurs de fonctions liées aux diviseurs premiers consécutifs d'un entier, 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; alternative link.
Programs
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Mathematica
a[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, Numerator[Total[1 - Most[p]/Rest[p]]]]; Array[a, 100] -
PARI
a(n) = {my(p = factor(n)[,1]); numerator(sum(i = 1, #p-1, 1 - p[i]/p[i+1]));}