Difference between revisions 16542038 and 17788856 on enwiki

A '''Zeisel number''' is a [[square-free]] [[integer]] ''k'' with at least three [[prime factor]]s which fall into the pattern 

:<math>p_x = ap_{x - 1} + b</math>

where ''a'' and ''b'' are fixed constants and ''x'' is the index number of each prime factor in the factorization, sorted from lowest to highest. For the purpose of determining Zeisel numbers, <math>p_0 = 1</math>. The first few Zeisel numbers are

:[[105 (number)|105]], 1419, [[1729 (number)|1729]], 1885, 4505, 5719, 15387, 24211, 25085, 27559, 31929, 54205, 59081, 114985, 207177, 208681, 233569, 287979, 294409, 336611, 353977, 448585, 507579, 982513, 1012121, 1073305, 1242709, 1485609, 2089257, 2263811, 2953711

{{OEIS|id=A051015}}. To give an example, 1729 is a Zeisel number with the constants ''a'' = 1 and ''b'' = 6, its factors being 7, 13 and 19, falling into the pattern

:<math>p_1 = 7, p_1 = 1p_0 + 6</math>
:<math>p_2 = 13, p_2 = 1p_1 + 6</math>
:<math>p_3 = 19, p_3 = 1p_2 + 6</math>

(contracted; show full)*[http://www.research.att.com/projects/OEIS?Anum=A051015 Sloane Sequence A051015]
*[http://mathworld.wolfram.com/ZeiselNumber.html MathWorld article]
*[http://www.mathpages.com/home/kmath015.htm MathPages article]

[[Category:Number sequences]]

[[de:Zeisel-Zahl]]
[[fr:Nombre de Zeisel]]