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