Displaying similar documents to “Remarks on generalized Ramanujan sums and even functions.”

An arithmetic formula of Liouville

Erin McAfee, Kenneth S. Williams (2006)

Journal de Théorie des Nombres de Bordeaux

Similarity:

An elementary proof is given of an arithmetic formula, which was stated but not proved by Liouville. An application of this formula yields a formula for the number of representations of a positive integer as the sum of twelve triangular numbers.

Evaluation of divisor functions of matrices

Gautami Bhowmik (1996)

Acta Arithmetica

Similarity:

1. Introduction. The study of divisor functions of matrices arose legitimately in the context of arithmetic of matrices, and the question of the number of (possibly weighted) inequivalent factorizations of an integer matrix was asked. However, till now only partial answers were available. Nanda [6] evaluated the case of prime matrices and Narang [7] gave an evaluation for 2×2 matrices. We obtained a recursion in the size of the matrices and the weights of the divisors [1,2] which helped...