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A344422 Palindromes having more divisors than all smaller palindromes. 5
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 (list; graph; refs; listen; history; text; internal format)
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
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Data corrected and extended by David A. Corneth, May 18 2021
STATUS
approved

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Last modified April 20 21:11 EDT 2024. Contains 371845 sequences. (Running on oeis4.)