Gabriel Mincu and Laurentiu Panaitopol:On some properties of squarefree and squareful numbers, p.63-68

Abstract:

A number is called squareful if it contains at least a square in its prime factorization.We study the integers that can be written as sums of two squarefree numbers, as sums of two squareful numbers and as sums of a squarefree and a squareful number. We also show that between $n^2$ and $(n+1)^2$ there are more than $n$ squarefree numbers.

Key Words: Squarefree numbers, squareful numbers, additive representations.

2000 Mathematics Subject Classification: Primary: 11A67,
Secondary: 11N25, 11N80.

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