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%I #25 Sep 21 2023 18:26:12
%S 1,2,3,4,5,7,333,17571,1757571,1787871,2249422,4369634,5136315,
%T 412727214,439838934,518686815,541626145,17575757571,52554845525,
%U 4166253526614,5136813186315,5136868686315,5806270726085,7359770779537,172757272757271,513636363636315
%N Palindromes whose sum of divisors is palindromic.
%C a(39) >= 10^18. - _Hiroaki Yamanouchi_, Sep 27 2014
%C Intersection of A002113 and of A028980. - _Michel Marcus_, Apr 06 2015
%H Hiroaki Yamanouchi, <a href="/A028986/b028986.txt">Table of n, a(n) for n = 1..38</a>
%H P. De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>
%t 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 *)
%t 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 *)
%o (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
%o pal(n)=d=digits(n);Vecrev(d)==d
%o for(n=2,10^5,if(pal(sigma(a(n))),print1(a(n),", "))) \\ _Derek Orr_, Apr 05 2015
%Y Cf. A002113 (palindromes), A028980 (sigma(n) is a palindrome).
%K nonn,base
%O 1,2
%A _Patrick De Geest_
%E a(18)-a(24) from _Donovan Johnson_, Apr 19 2010
%E a(25)-a(26) from _Donovan Johnson_, Jun 16 2011
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