A088001 a(n) is the sum of non-palindromic divisors of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 12, 13, 14, 15, 16, 17, 18, 19, 30, 21, 0, 23, 36, 25, 39, 27, 42, 29, 55, 31, 48, 0, 51, 35, 66, 37, 57, 52, 70, 41, 77, 43, 0, 60, 69, 47, 100, 49, 85, 68, 91, 53, 99, 0, 98, 76, 87, 59, 147, 61, 93, 84, 112, 78, 0, 67, 119, 92, 129, 71, 162, 73

Offset: 1

Author

Labos Elemer, Oct 14 2003

Keywords

• base
• nonn

Links

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

Crossrefs

Cf. A087999, A088000, A088002.

Programs

Maple

A088001 := proc(n)
        numtheory[sigma](n)-A088000(n) ;
end proc; # R. J. Mathar, Jul 28 2016

Mathematica

Table[Plus @@ Select[Divisors[k], Reverse[x = IntegerDigits[#]] != x &], {k, 73}] (* Jayanta Basu, Aug 12 2013 *)
Table[Total[Select[Divisors[n],!PalindromeQ[#]&]],{n,80}] (* Harvey P. Dale, May 15 2025 *)

Python

def ispal(n):
    return n==int(str(n)[::-1])
def A088001(n):
    s=0
    for i in range(1, n+1):
        if n%i==0 and not ispal(i):
             s+=i
    return s # Indranil Ghosh, Feb 10 2017

Formula

a(n)=0 iff all divisors are palindromic. See A062687.

a(n)+A088000(n) = A000203(n). - R. J. Mathar, Sep 09 2015