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.

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, 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, 1, 31, 7, 1, 13, 33, 1, 17, 23, 35, 1, 3, 1, 37, 5, 19, 11, 39, 1

Offset: 1

Author

Amiram Eldar, Mar 03 2025

Keywords

• nonn
• easy
• frac

Comments

First differs from A119288 at n = 30.

First differs from {A226040(n-1)} at n = 35.

Also denominators of the fractions whose numerators are A381641.

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.

Crossrefs

Cf. A001221, A119288, A226040, A381638 (numerators), A381640, A381641.

Programs

Mathematica

a[n_] := Module[{p = FactorInteger[n][[;; , 1]]}, Denominator[Total[Most[p]/Rest[p]]]]; Array[a, 100]

PARI

a(n) = {my(p = factor(n)[,1]); denominator(sum(i = 1, #p-1, p[i]/p[i+1]));}