Zeisel Number

A number  where the s are distinct primes and  such that

(1)

for , 2, ..., ,  taken as 1, and with  and  some fixed integers. For example,  is a Zeisel number with  since

(2)

as is  since

(3)

The first few Zeisel numbers are 105, 1419, 1729, 1885, 4505, ... (OEIS A051015), which correspond to constants (1, 2), (4, ), (1, 6), (2, 3), (3, 2), ....

REFERENCES:

MathPages. "Zeisel Numbers." https://www.mathpages.com/home/kmath015.htm.

Sloane, N. J. A. Sequence A051015 in "The On-Line Encyclopedia of Integer Sequences."