A087991 Number of non-palindromic divisors of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 0, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 0, 2, 2, 1, 4, 1, 3, 2, 3, 1, 3, 0, 3, 2, 2, 1, 6, 1, 2, 2, 3, 2, 0, 1, 3, 2, 4, 1, 5, 1, 2, 3, 3, 0, 4, 1, 5, 2, 2, 1, 6, 2, 2, 2, 0, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 0, 5, 0, 4, 1, 4, 4

Offset: 1

Author

Labos Elemer, Oct 08 2003

Keywords

• nonn
• base

Examples

			For n = 132: divisors = {1,2,3,4,6,11,12,22,33,44,66,132}, revdivisors = {1,2,3,4,6,11,21,22,33,44,66,231}, two of the 12 divisors of n are non-palindromic: {21,132}, so a(132) = 2.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A087990, A062687.

Cf. A001620, A118031.

Programs

Mathematica

palQ[n_] := Reverse[x = IntegerDigits[n]] == x; Table[Count[Divisors[n], ?(! palQ[#] &)], {n, 105}] (* _Jayanta Basu, Aug 10 2013 *)

Python

def ispal(n):
    w=str(n)
    return w==w[::-1]
def A087991(n):
    s = 0
    for i in range(1, n+1):
        if n%i==0 and not ispal(i):
            s+=1
    return s
print([A087991(n) for n in range(1,60)]) # Indranil Ghosh, Feb 10 2017

Formula

a(n) = A000005(n) - A087990(n).

Sum_{k=1..n} a(k) ~ n * (log(n) + c), where c = 2*A001620 - 1 - A118031 = -3.2158519... . - Amiram Eldar, Apr 17 2025