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

With a program by Joe)

If we are to find a 24-digit peculiar number, the most "non-one" digits could be 5, since 2^6-12 is more than 24. Just running the program for a=2 to 9, b=2 to 9, up to e=2 to 9, would suffice to disprove the idea that there are peculiar numbers of any length.