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

%I A343735 #26 Jul 15 2021 03:06:37
%S A343735 1,3,9,33,99,525,3003,5445,5775,50505,53235,171171,525525,5073705,
%T A343735 18999981,50555505,51666615,512272215,513828315,5026226205,5053553505,
%U A343735 5184994815,5708778075,52252425225,502299992205,502875578205,524241142425,579024420975
%N A343735 Odd palindromes having more divisors than all smaller odd palindromes.
%C A343735 A000005(a(n)) = A343736(n).
%C A343735 Conjectures:
%C A343735 (1) All terms after a(1)=1 are multiples of 3.
%C A343735 (2) The number of terms after a(30)=34418522581443 that are not multiples of 5 is finite but not zero.
%H A343735 Jon E. Schoenfield, <a href="/A343735/b343735.txt">Table of n, a(n) for n = 1..49</a>
%e A343735                                                       no. of
%e A343735    n        a(n)  prime factorization                divisors
%e A343735   --  ----------  ---------------------------------  --------
%e A343735    1           1  -                                         1
%e A343735    2           3  3                                         2
%e A343735    3           9  3^2                                       3
%e A343735    4          33  3 * 11                                    4
%e A343735    5          99  3^2 * 11                                  6
%e A343735    6         525  3 * 5^2 * 7                              12
%e A343735    7        3003  3 * 7 * 11 * 13                          16
%e A343735    8        5445  3^2 * 5 * 11^2                           18
%e A343735    9        5775  3 * 5^2 * 7 * 11                         24
%e A343735   10       50505  3 * 5 * 7 * 13 * 37                      32
%e A343735   11       53235  3^2 * 5 * 7 * 13^2                       36
%e A343735   12      171171  3^2 * 7 * 11 * 13 * 19                   48
%e A343735   13      525525  3 * 5^2 * 7^2 * 11 * 13                  72
%e A343735   14     5073705  3^3 * 5 * 7^2 * 13 * 59                  96
%e A343735   15    18999981  3^3 * 7 * 11 * 13 * 19 * 37             128
%e A343735   16    50555505  3 * 5 * 7^2 * 11 * 13^2 * 37            144
%e A343735   17    51666615  3^2 * 5 * 7 * 11 * 13 * 31 * 37         192
%e A343735   18   512272215  3^3 * 5 * 7^3 * 13 * 23 * 37            256
%e A343735   19   513828315  3^2 * 5 * 7 * 11^2 * 13 * 17 * 61       288
%e A343735   20  5026226205  3 * 5 * 7^2 * 11 * 13 * 17 * 29 * 97    384
%Y A343735 Cf. A000005, A002113 (palindromes), A076888 (their number of divisors), A029950 (odd palindromes), A344422, A345250, A343736.
%K A343735 nonn,base
%O A343735 1,2
%A A343735 _Jon E. Schoenfield_, Jun 22 2021