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A174282 a(n) = 3^n mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.

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%I A174282 #29 Jul 14 2025 22:52:35
%S A174282 0,1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,
%T A174282 0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,
%U A174282 0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0
%N A174282 a(n) = 3^n mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.
%C A174282 Appears to be always either 0 or 1.
%C A174282 This follows from Fermat's Little Theorem. - _Charles R Greathouse IV_, Feb 13 2011
%H A174282 G. C. Greubel, <a href="/A174282/b174282.txt">Table of n, a(n) for n = 1..1000</a>
%F A174282 a(n) = A000244(n) mod A014963(n).
%F A174282 a(n) = 1 if n = p^k for k > 0 and p a prime not equal to 3, a(n) = 0 otherwise. - _Charles R Greathouse IV_, Feb 13 2011
%t A174282 f[n_] := PowerMod[3, n - 1, Exp@ MangoldtLambda@ n]; Array[f, 105] (* _Robert G. Wilson v_, Jan 22 2015 *)
%t A174282 Table[Mod[3^(n-1) , E^(MangoldtLambda[n]) ], {n, 1, 100}] (* _G. C. Greubel_, Nov 25 2015 *)
%o A174282 (PARI) vector(95,n,ispower(k=n,,&k);isprime(k)&k!=3) \\ _Charles R Greathouse IV_, Feb 13 2011
%Y A174282 Cf. A174275, A062174.
%K A174282 nonn,easy
%O A174282 1,1
%A A174282 _Mats Granvik_, Mar 15 2010
%E A174282 More terms from _Robert G. Wilson v_, Jan 22 2015