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

Author

Reinhard Zumkeller, May 07 2003

Keywords

• nonn
• base

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.
		

Crossrefs

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

Programs

Mathematica

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