[ May 1, 2022 ]
Operations with nine- & pandigital factors creating palindromes
Alexandru Petrescu

Find all ninedigital/pandigital numbers having the following property :
Both sum and product of the prime factors (without multiplicity) are palindromic.

There are 8 solutions for the pandigitals and only one for the ninedigitals.
Note the two pandigital duplicates (#2 & #6) and (#7 & #8).

Here is some Pari/gp code to reproduce Alexandru's results.

{
for(n=1,10!, d=numtoperm(10, n+10!-1);
a=sum(i=1, #d, (d[i]-1)*10^(#d-i));
f=factor(a); sf=0; mf=1;
for(j=1,#f~, sf+=f[j,1]; mf*=f[j,1]);
dsf=digits(sf); dmf=digits(mf); 
if(Vecrev(dsf)==dsf && Vecrev(dmf)==dmf,
print(a," ",f," sum = ",sf,", product = ",mf));
);
}

The pandigital 4357812096 (#7) appears also in wonplate 26.
It is the product of these two palindromes :
69696 * 62526 = 4357812096