Definition:Powerful Number
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Theorem
A powerful number is a positive integer such that each of its prime factors appears with multiplicity at least $2$.
That is, each of its prime factors occurs at least squared.
Sequence
The sequence of powerful numbers begins:
- $1, 4, 8, 9, 16, 25, 27, 32, 36, 49, \ldots$
Also known as
A powerful number can also be referred to as a squareful, square full, square-full or 2-full number.
Also see
- Results about powerful numbers can be found here.
Sources
- 1970: Solomon W. Golomb: Powerful Numbers (Amer. Math. Monthly Vol. 77: pp. 848 – 855) www.jstor.org/stable/2317020
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $25$
- Weisstein, Eric W. "Powerful Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PowerfulNumber.html