Glasnik Matematicki, Vol. 49, No. 2 (2014), 351-367.

COMBINATORIAL CONVOLUTION SUMS DERIVED FROM DIVISOR FUNCTIONS AND FAULHABER SUMS

Bumkyu Cho, Daeyeoul Kim and Ho Park

National Institute for Mathematical Science , Yuseong-daero 1689-gil Daejeon 305-811, South Korea
e-mail: daeyeoul@nims.re.kr

Department of Mathematics, Dongguk University-Seoul,, 26 Pil-dong 3-ga Jung-gu Seoul, South Korea
e-mail: ph1240@dongguk.edu

Abstract.   It is known that certain convolution sums using Liouville identity can be expressed as a combination of divisor functions and Bernoulli numbers. In this article we find seven combinatorial convolution sums derived from divisor functions and Bernoulli numbers.

2010 Mathematics Subject Classification.   33E20, 11A67.

Key words and phrases.   Divisor functions, convolution sums, Faulhaber's sum.

DOI: 10.3336/gm.49.2.09

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