A083867 a(n) is the number of divisors of the n-th decimal palindrome that are palindromes.
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, 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, 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
Offset: 1
Examples
n=45, divisors of A002113(45)=363 are {1,3,11,33,121,363}, all are palindromes, therefore a(45)=A076888(45)=6.
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.
Programs
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Mathematica
ndp[n_]:=Count[Divisors[n],?(PalindromeQ[#]&)]; ndp/@Select[Range[ 2000],PalindromeQ] (* _Harvey P. Dale, Oct 29 2022 *)