numbers that are concatenation of its distinct prime divisors

[Giovanni Resta]

sven-h.simon wrote:
> Hello ,
> 
> there is already a sequence in the OEIS, take a look at sequences A083359 and 
> especially A083360, there are some more smaller numbers in A083360 than those 
> told by Giovanni Resta. It would be interesting for me, how Giovanni found those 
> larger numbers easily.

Tanya sequence and A083360 (a subsequence of A083359) are similar but not
identical. For example, the third element of A083360 does not fulfill Tanya
request. Indeed 13377 = 13*3*7^3, so there is a 7 too much in 13377.

For what concernes the large examples, I found them in this way:
I considered only numbers of the form p|q|3 == p*q*3^3 and p|q|5 =p*q*5^2, with p and q 
prime numbers and "|" meaning concatenation.
Assuming that q has n digits then we have (in the first case, the other is similar)
the following equation:
3+q*10+p*10^(n+1)= 3^3*p*q
which, for n fixed, is a quadratic diophantine equation that Mathematica
(or Alpern's on-line solver http://www.alpertron.com.ar/QUAD.HTM ) is
able to solve.
Repeating the process for various values of n and discarding the solutions
(p,q) which are not made of primes, one can easily find several large
numbers which satisfy Tanya's conditions.
giovanni.