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

1,20

Links

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

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005, A087990, A062687.

Cf. A001620, A118031.

Sequence in context: A333590 A263233 A300623 * A335451 A366078 A344652

Adjacent sequences: A087988 A087989 A087990 * A087992 A087993 A087994

Keyword

nonn,base

Author

Labos Elemer, Oct 08 2003

Status

approved