Evaluation of Convolution Sums asPn?€€€1m=1 mi(m)j(n ?€€€ m)

摘要

We calculate some special convolution sums related to the odd divisors multiplied by the even divisors. Also according to the Ramanujan’s functions implying σ1(n), σ3(n), and σ5(n), we obtain various convolution formulas.