A076888 a(n) is the number of divisors of the n-th positive palindromic number.

1, 2, 2, 3, 2, 4, 2, 4, 3, 2, 4, 4, 6, 4, 8, 4, 8, 6, 2, 4, 3, 2, 4, 2, 4, 6, 2, 2, 4, 6, 8, 8, 6, 18, 4, 10, 8, 6, 4, 2, 4, 6, 4, 2, 6, 2, 2, 4, 6, 12, 8, 8, 12, 4, 10, 8, 9, 8, 4, 4, 12, 4, 4, 8, 4, 6, 12, 8, 8, 16, 4, 12, 8, 10, 12, 9, 8, 16, 4, 4, 2, 4, 6, 2, 4, 8, 2, 2, 8, 4, 18, 4, 10, 16, 12, 4

Offset: 1

Author

Shyam Sunder Gupta, Nov 25 2002

Keywords

• base
• nonn

Examples

			a(11) = 4 because there are 4 divisors of 11th positive palindromic number (i.e., 22).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A002113.

Programs

Mathematica

palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; DivisorSigma[ 0,#]&/@ Select[Range[1000],palQ] (* Harvey P. Dale, Nov 29 2014 *)

Python

from sympy import divisor_count
def A076888(n):
    y = 10*(x:=10**(len(str(n+1>>1))-1))
    return divisor_count(int((c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1Chai Wah Wu, Jul 24 2024

Formula

a(n) = A000005(A002113(n+1)).