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

1,2

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.

Links

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

Example

                                                      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

Crossrefs

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

Sequence in context: A281973 A219557 A094538 * A037129 A148987 A176812

Adjacent sequences: A343732 A343733 A343734 * A343736 A343737 A343738

Keyword

nonn,base

Author

Jon E. Schoenfield, Jun 22 2021

Status

approved