For any rational integer , let be the number of squarefree (positive) integer such that the ideal class group of the imaginary quadratic number field contains an element of order . It is believed that for some positive constant , however the asymptotic formula for is still unknown except for the case , in which case we easily see by genus theory. The author improves the best known result for general due to M. Ram Murty [Topics in number theory, Kluwer Math. Appl., Dordr. 467, 229–239 (1999; Zbl 0993.11059)] to
(Note that for odd , we have .) He also offers a simple proof of .