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(2): Peculiars vs. Primes by Dej Mar)
Dej Mar, your reasoning for comparing two infinite sets is a bit
faulty. Consider the set of naturals (positive integers) and the set of
all integers. They are considered to have as many elements (even if one
of them is a strict subset of the other) because you can create a
one-to-one mapping from one set to the other. Being a subset does not
imply having less elements if you're talking about infinite sets. For
example, the number of rational numbers is also the same as the number
of integers. Very fascinating stuff :-).
Except for this detail, I agree with your statement: there are
differences between infinities, and probably there are more primes than
peculiars.
re(3): Peculiars vs. Primes
