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

1,2

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)

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

Formula

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

Example

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

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 *)

Prog

(C#) See C# link // Jon E. Schoenfield, Jun 19 2021
(PARI) See PARI link \\ David A. Corneth, May 18 2021

Crossrefs

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

Sequence in context: A173818 A263541 A283157 * A084324 A329529 A333456

Adjacent sequences: A344419 A344420 A344421 * A344423 A344424 A344425

Keyword

nonn,base

Author

Bhupendra Kumar Singh, May 17 2021

Extensions

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

Status

approved