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

%I A378140 #11 Jan 10 2025 12:06:22
%S A378140 1,4,6,232,44,636,66,484,888,616,2442,2112,4224,6006,2772,26862,23232,
%T A378140 232232,46464,297792,66066,88088,222222,252252,213312,21122112,234432,
%U A378140 606606,828828,444444,279972,21211212,666666,2444442,2114112,2578752,888888,4228224,42422424,23555532,54999945,82711728
%N A378140 a(n) is the least palindrome that has exactly n palindromic divisors other than itself and 1.
%e A378140 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.
%p A378140 ispali:= proc(n) rev(n) = n end proc:
%p A378140 g:= proc(x) nops(select(ispali,numtheory:-divisors(x) minus {1,x})) end proc:
%p A378140 F:= proc(m)
%p A378140    local x1,x2,x3;
%p A378140    if m::even then
%p A378140      [seq(seq(rev(x1) + 10^(m/2)*x1, x1 = 10^(m/2-1) .. 10^(m/2)-1))]
%p A378140    else
%p A378140      [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)];
%p A378140    fi
%p A378140 end proc:
%p A378140 N:= 50: # for a(0) .. a(N)
%p A378140 V:= Array(0..N): count:= 0:
%p A378140 for d from 1 while count <N+1 do
%p A378140   for x in F(d) while count < N+1 do
%p A378140     v:= g(x);
%p A378140     if v <= N and V[v] = 0 then V[v]:= x; count:= count+1;  fi
%p A378140 od od:
%p A378140 convert(V,list);
%Y A378140 Cf. A071276, A071277, A087997.
%K A378140 nonn,base
%O A378140 0,2
%A A378140 _Robert Israel_, Jan 08 2025