## powerful numberAlso known as a squarefull number, a positive whole number
n such that for every prime number
p dividing n, p^{2} also divides n.
Every powerful number can be written as a^{2}b^{3},
where a and b are positive integers. The first 20 powerful
numbers 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125,
128, 144, and 169. There are pairs of consecutive powerful numbers, such
as (8,9), (288,289), and (675,676). However, no three consecutive powerful
numbers are known and, in 1978, Paul Erdös
conjectured that none exist. ## Related category• TYPES OF NUMBERS | |||||

Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Alternative Energy • Contact |