A326929 Numbers whose divisors and arithmetic mean of divisors are palindromic.

1, 3, 5, 6, 7, 11, 22, 131, 262, 13331, 26662, 1333331, 2666662

Offset: 1

Author

Ivan N. Ianakiev, Oct 22 2019

Keywords

• nonn
• base
• hard
• more

Comments

a(14) is greater than 10^18 and at most (10^94-1)*(4/3)-1. - Charles R Greathouse IV, Oct 28 2019

(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

Examples

			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.
		

Crossrefs

Subsequence of A062687 and hence of A002113.

Subsequence of A003601.

Cf. A259050.

Programs

Mathematica

palQ[n_]:=ToString[n]==StringReverse[ToString[n]];
fQ[n_]:=palQ[Mean[Divisors[n]]]&&Union[palQ/@Divisors[n]]=={True};
Select[Range[2666662],fQ]