A378140 a(n) is the least palindrome that has exactly n palindromic divisors other than itself and 1.

1, 4, 6, 232, 44, 636, 66, 484, 888, 616, 2442, 2112, 4224, 6006, 2772, 26862, 23232, 232232, 46464, 297792, 66066, 88088, 222222, 252252, 213312, 21122112, 234432, 606606, 828828, 444444, 279972, 21211212, 666666, 2444442, 2114112, 2578752, 888888, 4228224, 42422424, 23555532, 54999945, 82711728

Offset: 0

Author

Robert Israel, Jan 08 2025

Keywords

• nonn
• base

Examples

			a(4) = 44 because 44 is a palindrome with exactly 4 palindromic divisors other than itself and 1, namely 2, 4, 11 and 22, and no smaller palindrome works.
		

Crossrefs

Cf. A071276, A071277, A087997.

Programs

Maple

ispali:= proc(n) rev(n) = n end proc:
g:= proc(x) nops(select(ispali,numtheory:-divisors(x) minus {1,x})) end proc:
F:= proc(m)
   local x1,x2,x3;
   if m::even then
     [seq(seq(rev(x1) + 10^(m/2)*x1, x1 = 10^(m/2-1) .. 10^(m/2)-1))]
   else
     [seq(seq(rev(x1) + 10^((m-1)/2)*x2 + 10^((m+1)/2)*x1,x2=0..9),x1=10^((m-1)/2-1)..10^((m-1)/2)-1)];
   fi
end proc:
N:= 50: # for a(0) .. a(N)
V:= Array(0..N): count:= 0:
for d from 1 while count