On ๐-free integers with small prime factors
On ๐-free integers with small prime factors
The object of this note is to give a nontrivial lower estimate for the function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi Subscript k Baseline left-parenthesis x comma y semicolon h right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ฯ<!-- ฯ --></mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>;</mml:mo> <mml:mi>h</mml:mi> <mml:mo stretchy="false">)</mml:mo> โฆ