A088000 - OEIS

%I #29 May 01 2021 08:03:19

%S 1,3,4,7,6,12,8,15,13,8,12,16,1,10,9,15,1,21,1,12,11,36,1,24,6,3,13,

%T 14,1,17,1,15,48,3,13,25,1,3,4,20,1,19,1,84,18,3,1,24,8,8,4,7,1,21,72,

%U 22,4,3,1,21,1,3,20,15,6,144,1,7,4,15,1,33,1,3,9,7,96,12,1,20,13,3,1,23,6,3

%N a(n) is the sum of the palindromic divisors of n.

%H Indranil Ghosh, <a href="/A088000/b088000.txt">Table of n, a(n) for n = 1..10000</a>

%e n=14: a(14)=1+2+7=10;

%e n=101: a(101)=1+101=102;

%p A088000 := proc(n)

%p     a := 0 ;

%p     for d in numtheory[divisors](n) do

%p         if isA002113(d) then

%p             a := a+d ;

%p         end if;

%p     end do;

%p     a ;

%p end proc:

%p seq(A088000(n),n=1..100) ; # _R. J. Mathar_, Sep 09 2015

%t Table[Plus @@ Select[Divisors[k], Reverse[x = IntegerDigits[#]] == x &], {k, 86}] (* _Jayanta Basu_, Aug 12 2013 *)

%o (Python)

%o def ispal(n):

%o     return n==int(str(n)[::-1])

%o def A088000(n):

%o     s=0

%o     for i in range(1, n+1):

%o         if n%i==0 and ispal(i):

%o              s+=i

%o     return s

%o print([A088000(n) for n in range(1,30)]) # _Indranil Ghosh_, Feb 10 2017

%o (PARI) a(n) = sumdiv(n, d, my(dd=digits(d)); if (Vecrev(dd) == dd, d)); \\ _Michel Marcus_, Apr 06 2020

%Y Cf. A062687 (all divisors are palindromic), A087990 (number of palindromic divisors).

%K base,nonn

%O 1,2

%A _Labos Elemer_, Oct 14 2003