document.write( "Question 618064: How many positive integers have exactly 3 proper divisors, each of which is less than 50? ( A proper divisor of a positive integer n is a positive integer divisor of n other than n itself.) \n" ); document.write( "
Algebra.Com's Answer #388736 by Edwin McCravy(20056)\"\" \"About 
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document.write( "There are exactly two kinds of positive integers which have \r\n" );
document.write( "exactly 3 proper divisors.  They are as follows:\r\n" );
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document.write( "1.  The cube of a prime p has 3 proper divisors 1, p, and pē.\r\n" );
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document.write( "2.  The product of a pair of unique primes p1, p2 has 3 proper \r\n" );
document.write( "divisors 1, p1, and p2.\r\n" );
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document.write( "There are 15 primes less than 50, which are\r\n" );
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document.write( "2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\r\n" );
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document.write( "The number of cubes of a prime less that 50 is the number of\r\n" );
document.write( "primes less than 50 which is also 15.\r\n" );
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document.write( "The number of products of a pair of unique primes less than 50 \r\n" );
document.write( "is the number of pairs of primes less than 50 which is 15C2 or\r\n" );
document.write( "\"15%2A14%2F2\" = 105\r\n" );
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document.write( "The total is 15 + 105 or 120.\r\n" );
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document.write( "Edwin
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