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

1, 5, 9972894583, 449853889404077636694265177903207995382439448590987815041588427345865911961016023550064137351211162870609

Offset

2,2

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.

Links

Table of n, a(n) for n=2..5.

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.

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A052000 A094467 A242828 * A324220 A273941 A067483

Adjacent sequences: A177161 A177162 A177163 * A177165 A177166 A177167

Keyword

nonn

Author

Alexander Adamchuk, May 04 2010

Status

approved