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

2, 4, 8, 88, 252, 2576, 8820, 2112, 4224, 8448, 44544, 48384, 846720, 4078080, 405504, 4091904, 441606144, 405909504, 886898688, 677707776, 4285005824, 63769149440, 21128282112, 633498894336, 2701312131072, 6739855589376, 29142024192, 65892155129856, 4815463645184, 445488555884544, 23088546155855872

Offset: 1

Author

Derek Orr, Mar 24 2014

Keywords

• nonn
• base

Comments

For all terms thus far, both m and reverse(m) are even.

a(24) > 10^11. - Giovanni Resta, Mar 31 2014

Examples

			2576 = 2*2*2*2*23*7 (6 factors)
6752 = 2*2*2*2*2*211 (6 factors)
Since 2576 is the smallest number with this property, a(6) = 2576.
		

Crossrefs

Cf. A237912, A237913.

Programs

Maple

A239697 := proc(n)
    local a;
    for a from 1 do
        if numtheory[bigomega](a) = n then
            if numtheory[bigomega](digrev(a)) =n then
                return a;
            end if;
        end if;
    end do:
end proc: # R. J. Mathar, Apr 04 2014

Python

import sympy
from sympy import factorint
from sympy import primorial
def Rev(x):
  rev = ''
  for i in str(x):
    rev = i + rev
  return int(rev)
def RevFact(x):
  n = 2
  while n <= primorial(x):
    if sum(list(factorint(n).values())) == x:
      if sum(list(factorint(Rev(n)).values())) == x:
        return n
      else:
        n += 1
    else:
      n += 1
x = 1
while x < 50:
  print(RevFact(x))
  x += 1

Formula

{min m: A001222(m) = A001222(A004086(m))}. - R. J. Mathar, Apr 04 2014

Extensions

a(17)-a(23) from Giovanni Resta, Mar 31 2014

a(24)-a(31) from David A. Corneth, Oct 03 2020