A093036 - OEIS

%I #35 Jan 22 2021 02:13:57

%S 1,2,4,6,12,24,66,132,264,792,1848,2772,5544,13332,14652,24024,26664,

%T 72072,79992,186648,205128,264264,559944,792792,1333332,2666664,

%U 7279272,7999992,13333320,14666652,26690664,29333304,80071992,134666532,269333064,807999192

%N Number of palindromic divisors of a(n) sets a new record.

%C Beginning with 132, it appears that all entries are congruent mod 11*12; 11 to produce palindromic divisors and 12 for numerous divisors. - _Robert G. Wilson v_, May 14 2004

%C The number of palindromic divisors of a(n) are 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 16, 19, 20, 21, 22, 24, 27, 28, 29, 30, 33, 37, 39, 43, 50, 52, 54, 57, 59, 61, 68, 72, 80, 90.

%C Every term is of the form Product_{i>=1} A226732(i)^e(i) for e(i) >= 0. - _David A. Corneth_, Jan 10 2021

%D Jason Earls, "Palindions," Mathematical Bliss, Pleroma Publications, 2009, pages 115-120. ASIN: B002ACVZ6O. [From _Jason Earls_, Nov 25 2009]

%H David A. Corneth, <a href="/A093036/a093036.gp.txt">Conjectured next terms</a>

%t palindromicQ[n_, b_:10] := If[FromDigits[Reverse[IntegerDigits[n, b]], b] == n, True, False]; a = 0; Do[c = Count[palindromicQ[ # ] & /@ Divisors[n], True]; If[c > a, Print[n]; a = c], {n, 300000000}] (* _Robert G. Wilson v_, May 14 2004 with a small modification from _Alonso del Arte_ to permit reuse in many other sequences' programs *)

%Y Cf. A087990, A002093, A226732.

%K nonn,base

%O 1,2

%A _Jason Earls_, May 08 2004

%E Edited and extended by _Robert G. Wilson v_, May 14 2004

%E a(35)-a(36) from _Chai Wah Wu_, Jan 21 2021