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A343735
Odd palindromes having more divisors than all smaller odd palindromes.
2
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
KEYWORD
nonn,base
AUTHOR
Jon E. Schoenfield, Jun 22 2021
STATUS
approved