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# Squareful

A number is squareful, also called nonsquarefree, if it contains at least one square in its prime factorization. The first few are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (OEIS A013929). The greatest multiple prime factors for the squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, ... (OEIS A046028). The least multiple prime factors for squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 2, ... (OEIS A046027).

No squareful Fibonacci numbers are known with prime.

The sequence of smallest terms in the first run of (at least) consecutive squareful integers for , 2, ... is 4, 8, 48, 242, 844, 22020, 217070, ... (OEIS A045882).

Greatest Prime Factor, Least Prime Factor, Smarandache Near-to-Primorial Function, Squarefree

## References

Sloane, N. J. A. Sequences A013929, A045882, A046027, and A046028 in "The On-Line Encyclopedia of Integer Sequences."

Squareful

## Cite this as:

Weisstein, Eric W. "Squareful." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Squareful.html