<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.2900.2963" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2>Let f be a multiplicative function
with</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>f(p) > f(p^k) > 1 (p prime, k >
1)</FONT></DIV>
<DIV><FONT face=Arial size=2>f(p) > f(q) > 1 (p, q prime, p <
q)</FONT></DIV>
<DIV> </DIV>
<DIV>then the record maxima of f occur at n# for n >= 1.</DIV></FONT></DIV>
<DIV> </DIV>
<DIV>Similarly, if</DIV>
<DIV> </DIV>
<DIV>0 < f(p) < f(p^k) < 1 (p prime, k > 1)</FONT></DIV>
<DIV><FONT face=Arial size=2>0 < f(p) < f(q) < 1 (p, q prime, p <
q).</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Then the record minima of f occur at n# for n >=
1.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Not deep theorems, but not well known and
definite time-savers.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Might be worth noting on A002110.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV></BODY></HTML>