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%I #7 Jul 04 2017 09:47:33
%S 1,1,2,4,6,60,60,120,144,7920,55440,18480,7920,27720,2520,637560,
%T 8288280,480720240,480720240,480720240,480720240,480720240,1442160720,
%U 9854764920,59128589520,59128589520,147821473800,670124014560
%N Least k > 0 such that t^k = 1 mod (prime(n) - t) for 0 < t < prime(n).
%C This sequence gives the period length of the base-p representation of HarmonicNumber[p-1]/p^2 (whose numerator is A061002).
%e a(5) = 6 because 2^6 = 1 mod 9, 3^6 = 1 mod 8, 4^6 = 1 mod 7, 5^6 = 1 mod 6, 6^6 = 1 mod 5, 7^6 = 1 mod 4, 8^6 = 1 mod 3, 9^6 = 1 mod 2 and 6 is the minimal exponent that satisfies this.
%t a[p_?PrimeQ] := Module[{e = 1}, While[! And @@ Table[Mod[PowerMod[i, e, p - i] - 1, p - i] == 0, {i, p - 1}], e++]; e]; a /@ Prime[Range[10]]
%K nonn
%O 1,3
%A Michael Ulm (taga(AT)hades.math.uni-rostock.de), Dec 18 2001
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