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

Peculiars vs. Primes by Eric)

For the first question: IF there are infinite "peculiar number n's" then there are as many as prime numbers... but you have to prove that there ARE infinite such numbers.

The second one is a even tougher one!