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

4, 6, 8, 9, 333, 646, 656, 979, 1001, 3553, 10801, 11111, 18581, 31713, 34943, 48484, 57375, 95259, 99099, 158851, 262262, 569965, 1173711, 1216121, 1399931, 1439341, 1502051, 1925291, 3203023, 3436343, 3659563, 3662663, 3803083, 3888883, 5185815, 5352535, 5893985, 5990995, 6902096, 9341439, 9452549

Offset: 1

Author

Derek Orr, Oct 03 2013

Keywords

• nonn
• base

Comments

All terms are composite numbers. - Chai Wah Wu, Dec 23 2015

Examples

			4 has proper divisors 1 and 2. 1 + 2 = 3 is also a palindrome. So 4 is a member of this sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..220

Crossrefs

Cf. A001065, A032350, A028986.

Programs

Mathematica

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; fQ[n_] := Block[{s = DivisorSigma[1, n] - n}, palQ@ s && s > 1]; Select[
Select[Range@ 1000000, palQ], fQ] (* Michael De Vlieger, Apr 06 2015 *)
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 *)

PARI

pal(n)=d=digits(n);Vecrev(d)==d
for(n=1,10^6,s=sigma(n)-n;if(pal(n)&&pal(s)&&s>1,print1(n,", "))) \\ Derek Orr, Apr 05 2015

Python

from sympy import divisors
def pal(n):
  r = ''
  for i in str(n):
    r = i + r
  return r == str(n)
{print(n,end=', ') for n in range(1,10**7) if pal(n) and pal(sum(divisors(n))-n) and len(divisors(n)) > 2}
## Simplified by Derek Orr, Apr 05 2015

Extensions

Initial terms 0 and 1 removed and more terms added by Derek Orr, Apr 05 2015

Definition edited by Derek Orr, Apr 05 2015

Definition edited by Harvey P. Dale, Jan 03 2016