A326929 - OEIS

%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