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A177164
a(n) = (n^r - 1)/r^2, where r = (n^(n-1) - 1)/(n-1).
0
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.
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}]
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 04 2010
STATUS
approved