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• # Artykuł - szczegóły

## Colloquium Mathematicum

2014 | 134 | 2 | 193-209

## Expansions of binary recurrences in the additive base formed by the number of divisors of the factorial

EN

### Abstrakty

EN
We note that every positive integer N has a representation as a sum of distinct members of the sequence ${d(n!)}_{n≥1}$, where d(m) is the number of divisors of m. When N is a member of a binary recurrence $u = {uₙ}_{n≥1}$ satisfying some mild technical conditions, we show that the number of such summands tends to infinity with n at a rate of at least c₁logn/loglogn for some positive constant c₁. We also compute all the Fibonacci numbers of the form d(m!) and d(m₁!) + d(m₂)! for some positive integers m,m₁,m₂.

193-209

wydano
2014

### Twórcy

autor
• Mathematical Institute, UNAM Juriquilla, Juriquilla, 76230 Santiago de Querétaro, Querétaro de Arteaga, México
• School of Mathematics, University of the Witwatersrand, P.O. Box Wits 2050, Johannesburg, South Africa
autor
• The John Knopfmacher Centre, for Applicable Analysis and Number Theory, University of the Witwatersrand, P.O. Box Wits 2050, Johannesburg, South Africa