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%I #81 Dec 10 2021 22:57:40
%S 1,2,4,6,44,66,252,2112,2772,6336,27972,48384,219912,252252,696696,
%T 828828,2114112,4228224,21333312,42666624,63999936,234666432,
%U 2154664512,2329559232,4815995184,8402442048,21354645312,40362626304,63708380736,211887788112
%N Palindromes having more divisors than all smaller palindromes.
%C A000005(a(n)) = 1, 2, 3, 4, 6, 8, 18, 28, 36, 42, 48, 72, 96, 108, 128, 144, 168, 192, 336, 384, .... - _Felix Fröhlich_, May 19 2021
%C From _Jon E. Schoenfield_, Jun 22 2021: (Start)
%C There exists at least one m-digit term for every m in 1..22 except 21 (see the b-file).
%C Conjecture: all terms after a(1)=1 are even. (End)
%H Jon E. Schoenfield, <a href="/A344422/b344422.txt">Table of n, a(n) for n = 1..59</a> (all terms < 10^22)
%H David A. Corneth, <a href="/A344422/a344422.gp.txt">PARI program</a>
%H Jon E. Schoenfield, <a href="/A344422/a344422.cs.txt">C# program</a>
%F A000005(a(n)) = A345250(n).
%e Terms include: 4 (3 divisors); 6 (4 divisors); 44 (6 divisors); 66 (8 divisors); 252 (18 divisors).
%t pal=Union@Flatten[Table[r=IntegerDigits@n;FromDigits/@(Join[r,#]&/@{Reverse@r,Rest@Reverse@r}),{n,10^5}]];m=0;lst={};Do[s=DivisorSigma[0,k];If[s>m,AppendTo[lst,k];m=s],{k,pal}];lst (* _Giorgos Kalogeropoulos_, Dec 08 2021 *)
%o (C#) See C# link // _Jon E. Schoenfield_, Jun 19 2021
%o (PARI) See PARI link \\ _David A. Corneth_, May 18 2021
%Y Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A002182, A084324, A093036, A345250.
%K nonn,base
%O 1,2
%A _Bhupendra Kumar Singh_, May 17 2021
%E Data corrected and extended by _David A. Corneth_, May 18 2021
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