123 is a peculiar integer, because 1+2+3=1*2*3. 1412 is also peculiar, since 1+4+1+2=1*4*1*2.

A simple question: are there infinitely many such numbers?

A not so simple question: if so, are there such numbers for ANY number of digits?

(In reply to re: Peculiars vs. Primes by Federico Kereki)

Though both Peculiars and Primes may have infinite representatives, their "infinities" are not necessarily equal.  For example, there are an infinite number of fractions that exist between both 0 and 1 and 0 and 2, yet the same number of "infinite" fractions that exist between 0 and 1 also exist between 0 and 2, plus an additional number of "infinite" fractions exist between 1 and 2, therefore there are more "infinite" fractions between 0 and 2 than between 0 and 1.

To answer the question, then, of Peculiars and Primes, one would need to examine the frequency of the numbers as they progress from 1 to infinity.  My initial impression is that Primes exist more frequently than do Peculiar numbers.

Posted by Dej Mar on 2006-08-22 19:00:39