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A227947 Each term is a palindrome such that the sum of its proper divisors is a palindrome > 1.

%I A227947 #40 Oct 08 2024 17:37:44
%S A227947 4,6,8,9,333,646,656,979,1001,3553,10801,11111,18581,31713,34943,
%T A227947 48484,57375,95259,99099,158851,262262,569965,1173711,1216121,1399931,
%U A227947 1439341,1502051,1925291,3203023,3436343,3659563,3662663,3803083,3888883,5185815,5352535,5893985,5990995,6902096,9341439,9452549
%N A227947 Each term is a palindrome such that the sum of its proper divisors is a palindrome > 1.
%C A227947 All terms are composite numbers. - _Chai Wah Wu_, Dec 23 2015
%H A227947 Chai Wah Wu, <a href="/A227947/b227947.txt">Table of n, a(n) for n = 1..220</a>
%e A227947 4 has proper divisors 1 and 2. 1 + 2 = 3 is also a palindrome. So 4 is a member of this sequence.
%t A227947 palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; fQ[n_] := Block[{s = DivisorSigma[1, n] - n}, palQ@ s && s > 1]; Select[
%t A227947 Select[Range@ 1000000, palQ], fQ] (* _Michael De Vlieger_, Apr 06 2015 *)
%t A227947 spdQ[n_]:=Module[{spd=DivisorSigma[1,n]-n},n==IntegerReverse[n] && spd>1 && spd==IntegerReverse[spd]]; Select[Range[10^7],spdQ] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* _Harvey P. Dale_, Jan 03 2016 *)
%o A227947 (Python)
%o A227947 from sympy import divisors
%o A227947 def pal(n):
%o A227947   r = ''
%o A227947   for i in str(n):
%o A227947     r = i + r
%o A227947   return r == str(n)
%o A227947 {print(n,end=', ') for n in range(1,10**7) if pal(n) and pal(sum(divisors(n))-n) and len(divisors(n)) > 2}
%o A227947 ## Simplified by _Derek Orr_, Apr 05 2015
%o A227947 (PARI) pal(n)=d=digits(n);Vecrev(d)==d
%o A227947 for(n=1,10^6,s=sigma(n)-n;if(pal(n)&&pal(s)&&s>1,print1(n,", "))) \\ _Derek Orr_, Apr 05 2015
%Y A227947 Cf. A001065, A032350, A028986.
%K A227947 nonn,base
%O A227947 1,1
%A A227947 _Derek Orr_, Oct 03 2013
%E A227947 Initial terms 0 and 1 removed and more terms added by _Derek Orr_, Apr 05 2015
%E A227947 Definition edited by _Derek Orr_, Apr 05 2015
%E A227947 Definition edited by _Harvey P. Dale_, Jan 03 2016