References
-
A. Alaca, S. Alaca, and K. S. Williams, The convolution sum
${{\Sigma}_{l+24m=n}}^{{\sigma}(l){\sigma}(m)}$ and${{\Sigma}_{3l+8m=n}}^{{\sigma}(l){\sigma}(m)}$ , Math. J. Okayama Univ. 49 (2007), 93-111. -
A. Alaca, S. Alaca, and K. S. Williams, The convolution sum
${\Sigma}_{m{<}{\frac{n}{16}}^{{\sigma}(m){\sigma}(n-16m)}$ , Canad. Math. Bull. 51 (2008), no. 1, 3-14. https://doi.org/10.4153/CMB-2008-001-1 - B. C. Berndt, Ramanujan's Notebooks. Part II, Springer-Verlag, New York, 1989.
- Dario Castellanos, A note on bernoulli polynomials, Univ. de Carabobo, Valencia, Venezuela (1989), 98-102.
- J. W. L. Glaisher, On the square of the series in which the coefficients are the sums of the divisors of the exponents, Mess. Math. 14 (1884), 156-163.
- J. W. L. Glaisher, On certain sums of products of quantities depending upon the divisors of a number, Mess. Math. 15 (1885), 1-20.
- J. W. L. Glaisher, Expressions for the five powers of the series in which the coefficients are the sums of the divisors of the exponents, Mess. Math. 15 (1885), 33-36.
- H. Hahn, Convolution sums of some functions on divisors, Rocky Mountain J. Math. 37 (2007), no. 5, 1593-1622. https://doi.org/10.1216/rmjm/1194275937
- J. G. Huard, Z. M. Ou, B. K. Spearman, and K. S. Williams, Elementary evaluation of certain convolution sums involving divisor functions, Number theory for the millennium, II (Urbana, IL, 2000), 229-274, A K Peters, Natick, MA, 2002.
- D. Kim, A. Bayad, and N. Y. Ikikardes, Certain combinatoric convolution sums and their relations to Bernoulli and Euler Polynomials, J. Korean Math. Soc. 52 (2015), No. 3, pp. 537-565. https://doi.org/10.4134/JKMS.2015.52.3.537
- K. S. Williams, Number Theory in the Spirit of Liouville, London Mathematical Society, Student Texts 76, Cambridge, 2011.