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

1,2

Links

Table of n, a(n) for n=1..105.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A341946 A339915 A306509 * A076888 A357171 A355698

Adjacent sequences: A083864 A083865 A083866 * A083868 A083869 A083870

Keyword

nonn,base

Author

Reinhard Zumkeller, May 07 2003

Status

approved