%I #11 Oct 29 2022 11:45:47

%S 1,2,2,3,2,4,2,4,3,2,4,4,6,4,8,4,8,6,2,3,3,2,3,2,3,4,2,2,4,4,6,5,6,8,

%T 4,5,6,4,4,2,2,5,3,2,6,2,2,4,6,6,6,4,8,3,6,5,9,3,4,3,5,3,3,5,3,3,5,4,

%U 8,11,4,7,4,5,9,4,5,8,4,3,2,3,4,2,2,5,2,2,8,3,8,3,7,9,6,3,10,3,6,2,2,4,2,3,4

%N a(n) is the number of divisors of the n-th decimal palindrome that are palindromes.

%e n=45, divisors of A002113(45)=363 are {1,3,11,33,121,363}, all are palindromes, therefore a(45)=A076888(45)=6.

%e n=72, divisors of A002113(72)=636 are {1,2,3,4,6,12,53,106,159,212,318,636}, 7 of them are palindromes {1,2,3,4,6,212,636}, therefore a(72)=7 < A076888(72)=12.

%t ndp[n_]:=Count[Divisors[n],_?(PalindromeQ[#]&)]; ndp/@Select[Range[ 2000],PalindromeQ] (* _Harvey P. Dale_, Oct 29 2022 *)

%Y Cf. A083868, A083870, A076888, A000005, A002113.

%K nonn,base

%O 1,2

%A _Reinhard Zumkeller_, May 07 2003