A344422 Palindromes having more divisors than all smaller palindromes.

1, 2, 4, 6, 44, 66, 252, 2112, 2772, 6336, 27972, 48384, 219912, 252252, 696696, 828828, 2114112, 4228224, 21333312, 42666624, 63999936, 234666432, 2154664512, 2329559232, 4815995184, 8402442048, 21354645312, 40362626304, 63708380736, 211887788112

Offset: 1

Author

Bhupendra Kumar Singh, May 17 2021

Keywords

• nonn
• base

Comments

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

From Jon E. Schoenfield, Jun 22 2021: (Start)

There exists at least one m-digit term for every m in 1..22 except 21 (see the b-file).

Conjecture: all terms after a(1)=1 are even. (End)

Examples

			Terms include: 4 (3 divisors); 6 (4 divisors); 44 (6 divisors); 66 (8 divisors); 252 (18 divisors).
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..59 (all terms < 10^22)
• David A. Corneth, PARI program
• Jon E. Schoenfield, C# program

Crossrefs

Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A002182, A084324, A093036, A345250.

Programs

Mathematica

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 *)

PARI

\\ See PARI link. David A. Corneth, May 18 2021

Formula

A000005(a(n)) = A345250(n).

Extensions

Data corrected and extended by David A. Corneth, May 18 2021