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A239697 Smallest m such that m and reverse(m) each have n (not necessarily distinct) prime factors.

%I A239697 #35 May 22 2025 10:21:37
%S A239697 2,4,8,88,252,2576,8820,2112,4224,8448,44544,48384,846720,4078080,
%T A239697 405504,4091904,441606144,405909504,886898688,677707776,4285005824,
%U A239697 63769149440,21128282112,633498894336,2701312131072,6739855589376,29142024192,65892155129856,4815463645184,445488555884544,23088546155855872
%N A239697 Smallest m such that m and reverse(m) each have n (not necessarily distinct) prime factors.
%C A239697 For all terms thus far, both m and reverse(m) are even.
%C A239697 a(24) > 10^11. - _Giovanni Resta_, Mar 31 2014
%F A239697 {min m: A001222(m) = A001222(A004086(m))}. - _R. J. Mathar_, Apr 04 2014
%e A239697 2576 = 2*2*2*2*23*7 (6 factors)
%e A239697 6752 = 2*2*2*2*2*211 (6 factors)
%e A239697 Since 2576 is the smallest number with this property, a(6) = 2576.
%p A239697 A239697 := proc(n)
%p A239697     local a;
%p A239697     for a from 1 do
%p A239697         if numtheory[bigomega](a) = n then
%p A239697             if numtheory[bigomega](digrev(a)) =n then
%p A239697                 return a;
%p A239697             end if;
%p A239697         end if;
%p A239697     end do:
%p A239697 end proc: # _R. J. Mathar_, Apr 04 2014
%o A239697 (Python)
%o A239697 import sympy
%o A239697 from sympy import factorint
%o A239697 from sympy import primorial
%o A239697 def Rev(x):
%o A239697   rev = ''
%o A239697   for i in str(x):
%o A239697     rev = i + rev
%o A239697   return int(rev)
%o A239697 def RevFact(x):
%o A239697   n = 2
%o A239697   while n <= primorial(x):
%o A239697     if sum(list(factorint(n).values())) == x:
%o A239697       if sum(list(factorint(Rev(n)).values())) == x:
%o A239697         return n
%o A239697       else:
%o A239697         n += 1
%o A239697     else:
%o A239697       n += 1
%o A239697 x = 1
%o A239697 while x < 50:
%o A239697   print(RevFact(x))
%o A239697   x += 1
%Y A239697 Cf. A237912, A237913.
%K A239697 nonn,base
%O A239697 1,1
%A A239697 _Derek Orr_, Mar 24 2014
%E A239697 a(17)-a(23) from _Giovanni Resta_, Mar 31 2014
%E A239697 a(24)-a(31) from _David A. Corneth_, Oct 03 2020