with (in which is number of distinct prime factors function, and all the are prime divisors of , except purely as a notational convenience, and are sorted in ascending order) if each prime fits into the recurrence relation , with being some fixed integer multiplicand, and being some fixed integer addend, then is called a Zeisel number.
For example, . Say that and . This checks out: , and . 1419 is a Zeisel number. The first few Zeisel numbers are 105, 1419, 1729, 1885, 4505, 5719, … listed in A051015 of Sloane’s OEIS. The Carmichael numbers of the form are a subset of the Zeisel numbers; the constants are then and .
These numbers were first studied by Kevin Brown, who was searching for prime solutions to . Helmut Zeisel replied that 1885 is such an . Brown discovered that its prime factors fit the recurrrence relation with and . He called numbers fitting such a recurrence relation “Zeisel numbers” and the term has stuck, being taken up by the OEIS, MathWorld and Wikipedia. Zeisel himself has suggested the term “Brown-Zeisel number” but this has not caught on. There is a different concept of the Zeisel number used in chemistry.
|Date of creation||2013-03-22 17:44:03|
|Last modified on||2013-03-22 17:44:03|
|Last modified by||CompositeFan (12809)|