squarefull number

A natural number $n$ is called squarefull (or powerful) if for every prime $p|n$ we have $p^2|n$. In 1978 Erdős conjectured that we cannot have three consecutive squarefull natural numbers. If we assume the ABC Conjecture, there are only finitely many such consecutive triples.

Title	squarefull number
Canonical name	SquarefullNumber
Date of creation	2013-03-22 11:45:26
Last modified on	2013-03-22 11:45:26
Owner	KimJ (5)
Last modified by	KimJ (5)
Numerical id	10
Author	KimJ (5)
Entry type	Definition
Classification	msc 11A51
Classification	msc 55-00
Classification	msc 82-00
Classification	msc 83-00
Classification	msc 81-00
Classification	msc 39A99
Classification	msc 39B72
Classification	msc 33E30
Synonym	powerful number
Related topic	NFullNumber