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The distribution of square-full integers

Authors:	X. -D. Cao

Affiliation:	(1) Beijing Petro-chemical Engineering College, Daxing, 102600 Beijing, China

Abstract:	Let $Delta (x) = sumlimits_{n leqslant x} {f(n) - frac{{varsigma (3/2)}}{{varsigma (3)}}x^{1/2} - frac{{varsigma (2/3)}}{{varsigma (2)}}x^{1/3} }$ , wheref(n) is the characteristic function of square-full integers. A formula is proved that can be used to obtain better upper bound estimate for (x). We get (x)=O(x^5/33+), which improves the exponent 11/72 obtained by R. Blasubramania and K. Ramachandra.

Keywords:	Primary 11N13 Secondary 11L40
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