Squarefull numbers

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Squarefull numbers (powerful numbers) are numbers for which all the prime factors exponents are at least 2, while squareful numbers are numbers for which at least one of the prime factors exponents is 2, thus are not squarefree numbers.

A001694 Powerful numbers, definition (1): if a prime 

p

divides 

n

then 

p 2

must also divide 

n

(also called squarefull, square-full numbers, 2-full numbers or powerful numbers).

{1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, ...}

}

See also

• Squarefree numbers
• Squareful numbers