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A076888
a(n) is the number of divisors of the n-th positive palindromic number.
8
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
1,2
LINKS
FORMULA
a(n) = A000005(A002113(n+1)).
EXAMPLE
a(11) = 4 because there are 4 divisors of 11th positive palindromic number (i.e., 22).
MATHEMATICA
palQ[n_]:=Module[{idn=IntegerDigits[n]}, idn==Reverse[idn]]; DivisorSigma[ 0, #]&/@ Select[Range[1000], palQ] (* Harvey P. Dale, Nov 29 2014 *)
PROG
(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+1<x+y else (c:=n+1-y)*y+int(str(c)[::-1] or 0))) # Chai Wah Wu, Jul 24 2024
CROSSREFS
Sequence in context: A339915 A306509 A083867 * A357171 A355698 A087990
KEYWORD
base,nonn
AUTHOR
Shyam Sunder Gupta, Nov 25 2002
STATUS
approved