A028986 Palindromes whose sum of divisors is palindromic.

1, 2, 3, 4, 5, 7, 333, 17571, 1757571, 1787871, 2249422, 4369634, 5136315, 412727214, 439838934, 518686815, 541626145, 17575757571, 52554845525, 4166253526614, 5136813186315, 5136868686315, 5806270726085, 7359770779537, 172757272757271, 513636363636315

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

a(39) >= 10^18. - Hiroaki Yamanouchi, Sep 27 2014

Intersection of A002113 and of A028980. - Michel Marcus, Apr 06 2015

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..38
• P. De Geest, World!Of Numbers

Crossrefs

Cf. A002113 (palindromes), A028980 (sigma(n) is a palindrome).

Programs

Mathematica

palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; t={}; Do[If[palQ[n] && palQ[DivisorSigma[1,n]],AppendTo[t,n]],{n,5.2*10^6}]; t (* Jayanta Basu, May 17 2013 *)
Select[Range[52*10^6], AllTrue[{#, DivisorSigma[1, #]}, PalindromeQ] &] (* This naive program is not suitable for generating more than 13 terms of the sequence. *) (* Harvey P. Dale, Sep 21 2023 *)

PARI

a(n)=my(d,i,r);r=vector(#digits(n-10^(#digits(n\11)))+#digits(n\11));n=n-10^(#digits(n\11));d=digits(n);for(i=1,#d,r[i]=d[i];r[#r+1-i]=d[i]);sum(i=1,#r,10^(#r-i)*r[i]) \\ David A. Corneth in A002113, Jun 06 2014
pal(n)=d=digits(n);Vecrev(d)==d
for(n=2,10^5,if(pal(sigma(a(n))),print1(a(n),", "))) \\ Derek Orr, Apr 05 2015

Extensions

a(18)-a(24) from Donovan Johnson, Apr 19 2010

a(25)-a(26) from Donovan Johnson, Jun 16 2011