document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=914653>Question 914653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A proper divisor of a positive integer is a positive integral divisor other than 1 and itself. A positive integer greater than 1 is a sweet # if the product of its distinct proper divisors is equal to the # itself. List the 10 smallest sweet numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555217 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose the proper divisors of n are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d_1, \ldots, d_k\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 1 < d_1 < \ldots < d_k < n\">. Then we have <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d_1d_k = n\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large d_2d_{k-1} = n\">, and so on. We want the product of the d_i's to equal n, and this occurs if and only if n has two proper divisors (excluding 1), or when n has exactly four divisors. This occurs if and only if n is a product of two different primes, or n is the cube of a prime.\r<BR>\n" );
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document.write( "First 10 sweet numbers: 6, 8, 10, 14, 15, 21, 22, 26, 27, 33 </SPAN>\n" );
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