1. Smallest palindromes with exactly n palindromic prime factors
    (counted with multiplicity).
Report extensions also to Sloane's "Online Encyclopedia".
Refer to sequence A046385

npalindromepalindromic prime factors
01-
122
242 * 2
382 * 2 * 2
4882 * 2 * 2 * 11
52522 * 2 * 3 * 3 * 7
627722 * 2 * 3 * 3 * 7 * 11
7827282 * 2 * 2 * 3 * 3 * 3 * 383
821122 * 2 * 2 * 2 * 2 * 2 * 3 * 11
942242 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 11
1084482 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 11
112369896322 * 2 * 2 * 2 * 2 * 2 * 3 * 11 * 11 * 101 * 101
12483842 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 7
1329777922 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 727  
14??
15??

2. Smallest palindromes with exactly n prime factors
    (counted with multiplicity).
Refer to sequence A076886 [ November 25, 2002 ]
by Shyam Sunder Gupta (extended by Robert G. Wilson v).

npalindromeprime factors
01-
122
242 * 2
382 * 2 * 2
4882 * 2 * 2 * 11
52522 * 2 * 3 * 3 * 7
627722 * 2 * 3 * 3 * 7 * 11
7278722 * 2 * 2 * 2 * 2 * 13 * 67
821122 * 2 * 2 * 2 * 2 * 2 * 3 * 11
942242 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 11
1084482 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 11
11445442 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 29
12483842 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 * 7
1329777922 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 727  
14270110722 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 11 * 11 * 109
154055042 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 11
164091904212 * 33 * 37
17441606144213 * 3 * 7 * 17 * 151
18405909504212 * 32 * 7 * 112 * 13
19886898688216 * 3 * 13 * 347
20677707776216 * 33 * 383
214285005824219 * 11 * 743
22276486684672218 * 3 * 11 * 31 * 1031
2321128282112219 * 3 * 7 * 19 * 101
24633498894336217 * 3 * 74 * 11 * 61
252701312131072222 * 3 * 19 * 11299
268691508051968222 * 3 * 7 * 101 * 977

3. Smallest palindromes with exactly n distinct prime factors.
Report extensions also to Sloane's "Online Encyclopedia".
Refer to sequence A046399

npalindromedistinct prime factors
01-
122
262 * 3
3662 * 3 * 11
48582 * 3 * 11 * 13
560062 * 3 * 7 * 11 * 13
62222222 * 3 * 7 * 11 * 13 * 37
7224444222 * 3 * 7 * 11 * 13 * 37 * 101
82448684422 * 3 * 7 * 13 * 17 * 23 * 31 * 37
964347743462 * 3 * 7 * 11 * 13 * 17 * 19 * 31 * 107  
10??
11??
12??
13??

4. Smallest palindromes with exactly n distinct palindromic prime factors.

npalindromedistinct palindromic prime factors
01-
122
262 * 3
3662 * 3 * 11
466662 * 3 * 11 * 101
5??
6??
7??

5. Palindromes divided by the palindromic sum of their prime factors
    (counted with multiplicity) is a palindrome.
Report extensions also to Sloane's "Online Encyclopedia".
Refer to sequence A046362

palindromeprime factorspalindromic sumpalindromic quotient
42 * 241
13454313 * 17 * 23 * 31 * 37 (all distinct)11112121
123333213 * 3 * 7 * 11 * 13 * 37 * 37111111111
14256652413 * 3 * 7 * 7 * 11 * 13 * 13 * 37 * 4714110111101
????
????

6. Palindromes divisible by the palindromic sum of their palindromic prime factors
    (counted with multiplicity).

palindromepalindromic prime factorspalindromic sumquotient
42 * 241
54453 * 3 * 5 * 11 * 1133165
????
????



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