A343735 Odd palindromes having more divisors than all smaller odd palindromes.

1, 3, 9, 33, 99, 525, 3003, 5445, 5775, 50505, 53235, 171171, 525525, 5073705, 18999981, 50555505, 51666615, 512272215, 513828315, 5026226205, 5053553505, 5184994815, 5708778075, 52252425225, 502299992205, 502875578205, 524241142425, 579024420975

Offset: 1

Author

Jon E. Schoenfield, Jun 22 2021

Keywords

• nonn
• base

Comments

A000005(a(n)) = A343736(n).

Conjectures:

(1) All terms after a(1)=1 are multiples of 3.

(2) The number of terms after a(30)=34418522581443 that are not multiples of 5 is finite but not zero.

Examples

			                                                      no. of
   n        a(n)  prime factorization                divisors
  --  ----------  ---------------------------------  --------
   1           1  -                                         1
   2           3  3                                         2
   3           9  3^2                                       3
   4          33  3 * 11                                    4
   5          99  3^2 * 11                                  6
   6         525  3 * 5^2 * 7                              12
   7        3003  3 * 7 * 11 * 13                          16
   8        5445  3^2 * 5 * 11^2                           18
   9        5775  3 * 5^2 * 7 * 11                         24
  10       50505  3 * 5 * 7 * 13 * 37                      32
  11       53235  3^2 * 5 * 7 * 13^2                       36
  12      171171  3^2 * 7 * 11 * 13 * 19                   48
  13      525525  3 * 5^2 * 7^2 * 11 * 13                  72
  14     5073705  3^3 * 5 * 7^2 * 13 * 59                  96
  15    18999981  3^3 * 7 * 11 * 13 * 19 * 37             128
  16    50555505  3 * 5 * 7^2 * 11 * 13^2 * 37            144
  17    51666615  3^2 * 5 * 7 * 11 * 13 * 31 * 37         192
  18   512272215  3^3 * 5 * 7^3 * 13 * 23 * 37            256
  19   513828315  3^2 * 5 * 7 * 11^2 * 13 * 17 * 61       288
  20  5026226205  3 * 5 * 7^2 * 11 * 13 * 17 * 29 * 97    384
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..49

Crossrefs

Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A029950 (odd palindromes), A344422, A345250, A343736.