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On the error term of the logarithm of the lcm of a quadratic sequence

Juanjo Rué; Paulius Šarka; Ana Zumalacárregui — 2013

Journal de Théorie des Nombres de Bordeaux

We study the logarithm of the least common multiple of the sequence of integers given by $1^{2} + 1, 2^{2} + 1, \dots, n^{2} + 1$ . Using a result of Homma [] on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo [].

On the sum of digits of some sequences of integers

Javier Cilleruelo; Florian Luca; Juanjo Rué; Ana Zumalacárregui — 2013

Open Mathematics

Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.

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