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

1,2

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

Links

Table of n, a(n) for n=1..13.

Example

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.

Mathematica

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

Crossrefs

Subsequence of A062687 and hence of A002113.

Subsequence of A003601.

Cf. A259050.

Sequence in context: A227026 A361827 A053272 * A138927 A030333 A081677

Adjacent sequences: A326926 A326927 A326928 * A326930 A326931 A326932

Keyword

nonn,base,hard,more

Author

Ivan N. Ianakiev, Oct 22 2019

Status

approved