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%I #26 Nov 01 2021 01:15:42
%S 1,2,7,39,311,3268,42799,672605,12345679,259374246,6140565047,
%T 161792257795,4696537119847,148943500129544,5124095576030431,
%U 190082780764323705,7563707819165039903,321380710796022350410,14523213296398891966759,695546073617378871592991
%N a(n) = (n^(n-1)-1)/(n-1)^2.
%C Written in base n, a(n) has n-2 digits and looks like 12345... except that the final digit is n-1 rather than n-2.
%C Note that 2^m-1 divides a(m+1) = ((m+1)^m-1)/m^2 if and only if m = 2^k-1 with gcd(k,m) = 1. Mersenne numbers M = 2^p-1 such that a(M+1)/(2^M-1) is prime are Mersenne primes 2^3-1 = 7 and 2^7-1 = 127. - _Thomas Ordowski_, Sep 19 2021
%H Harry J. Smith, <a href="/A060073/b060073.txt">Table of n, a(n) for n = 2..200</a>
%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>
%F a(n) = A037205(n-1)/(n-1)^2 = A060072(n)/(n-1) = A058128(n)/n = A059522(n)/A000142(n).
%e a(10) = 999999999/81 = 111111111/9 = 12345679.
%t Table[(n^(n - 1) - 1)/(n - 1)^2, {n, 2, 20}] (* _Michael De Vlieger_, Oct 28 2021 *)
%o (PARI) { for (n=2, 200, write("b060073.txt", n, " ", (n^(n - 1) - 1)/(n - 1)^2); ) } \\ _Harry J. Smith_, Jul 01 2009
%Y Cf. A000142, A037205, A058128, A059522, A060072, A127837 (numbers p such that a(p+1) is prime).
%K nonn
%O 2,2
%A _Henry Bottomley_, Feb 21 2001
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