Magic Series

A set of distinct numbers taken from the interval form a magic series if their sum is the th magic constant

(Kraitchik 1942, p. 143). The numbers of magic series of orders , 2, ..., are 1, 2, 8, 86, 1394, ... (OEIS A052456). The following table gives the first few magic series of small order.

	magic series
1
2	,
3	, , , , , , ,

If the sum of the th powers of these number is the magic constant of degree for all , then they are said to form a th order multimagic series. Here, the magic constant of degree is defined as times the sum of the first th powers,

where is a harmonic number of order .