We consider generalizations and analogues of Cesàro’s formula
åni=1 f((i, n)) = åd|n f(d)f(n/d)\sum^{n}_{i=1} f((i, n)) = \sum_{d|n} f(d)\phi(n/d), where (
i, n) denotes the greatest common divisor of
i and
n and where
f\phi is Euler’s totient function. Particular attention is paid to the unitary analogues of this formula.
Mathematics Subject Classification (2000). 11A25
Keywords. Cesàro’s theorem - Pillai’s function - arithmetical expression - unitary convolution - even functions modulo m
Manuscript received: February 11, 2007 and, in final form, July 17, 2007.