A177164 a(n) = (n^r - 1)/r^2, where r = (n^(n-1) - 1)/(n-1).

1, 5, 9972894583, 449853889404077636694265177903207995382439448590987815041588427345865911961016023550064137351211162870609

Offset: 2

Author

Alexander Adamchuk, May 04 2010

Keywords

• nonn

Comments

The next term has 1204 digits.

r = (n^(n-1) - 1)/(n-1) = A060072(n) is the (n-1)-digit repunit in base n.

r^2 divides n^r - 1 for all bases n > 1.

Examples

			a(10) = (10^111111111 - 1)/111111111^2.
		

Crossrefs

Cf. A060072, A127100, A127101, A127102, A127103, A127104, A127105, A127106, A127107, A127092.

Programs

Mathematica

Table[(n^((n^(n - 1) - 1)/(n - 1)) - 1)/((n^(n - 1) - 1)/(n - 1))^2, {n, 2, 6}]

Formula

a(n) = (n^((n^(n-1) - 1)/(n-1)) - 1)/((n^(n-1) - 1)/(n-1))^2.

a(n) = (n^A060072(n) - 1)/A060072(n)^2.