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

0,2

Links

Table of n, a(n) for n=0..41.

Example

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.

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 <N+1 do
  for x in F(d) while count < N+1 do
    v:= g(x);
    if v <= N and V[v] = 0 then V[v]:= x; count:= count+1;  fi
od od:
convert(V, list);

Crossrefs

Cf. A071276, A071277, A087997.

Sequence in context: A081970 A076098 A377392 * A377390 A141568 A376381

Adjacent sequences: A378136 A378137 A378139 * A378141 A378142 A378143

Keyword

nonn,base

Author

Robert Israel, Jan 08 2025

Status

approved