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%I #19 Nov 18 2019 01:20:51
%S 1,3,5,6,7,11,22,131,262,13331,26662,1333331,2666662
%N Numbers whose divisors and arithmetic mean of divisors are palindromic.
%C a(14) is greater than 10^18 and at most (10^94-1)*(4/3)-1. - _Charles R Greathouse IV_, Oct 28 2019
%C (4*10^A259050(n)-7)/3 and (8*10^A259050(n)-14)/3 are terms. Conjecture: all terms > 10 are of these forms. - _Chai Wah Wu_, Nov 17 2019
%e The divisors of 2666662 are {1,2,1333331,2666662} which are all palindromic. Their arithmetic mean is 999999 and is also palindromic. Therefore, 2666662 is in the sequence.
%t palQ[n_]:=ToString[n]==StringReverse[ToString[n]];
%t fQ[n_]:=palQ[Mean[Divisors[n]]]&&Union[palQ/@Divisors[n]]=={True};
%t Select[Range[2666662],fQ]
%Y Subsequence of A062687 and hence of A002113.
%Y Subsequence of A003601.
%Y Cf. A259050.
%K nonn,base,hard,more
%O 1,2
%A _Ivan N. Ianakiev_, Oct 22 2019
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