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Least number such that n*k+1 is an n-th power.
2

%I #4 Dec 05 2013 19:55:47

%S 2,9,64,81,7776,15625,2097152,6561,262144,3486784401,743008370688,

%T 244140625,793714773254144,3937376385699289,1152921504606846976,

%U 43046721,2185911559738696531968,3814697265625

%N Least number such that n*k+1 is an n-th power.

%C a(n) <= {(n+1)^n - 1}/n.

%F a(n) = n*A076943(n) + 1.

%t Do[k = 2; While[ !IntegerQ[(k^n - 1)/n], k++ ]; Print[k^n], {n, 1, 19}]

%Y Cf. A076942, A076943, A074792.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Oct 19 2002

%E Edited, corrected and extended by _Robert G. Wilson v_, Oct 21 2002