A167284 - OEIS

%I #2 Mar 30 2012 17:34:35

%S 1,1,1,1,1,0,1,1,3,1,1,4,27,1,0,1,1,3,1,5,1,1,4,27,256,3125,1,0,1,4,

%T 27,1,5,36,343,1,1,4,27,256,3125,1,7,64,0,1,4,27,1,5,36,343,1,9

%N A triangular sequence related to the EulerPhi function: t(n,k)=If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]

%C Row sums are:

%C {1, 2, 2, 6, 33, 12, 3414, 418, 3485, 427,...}

%C The sequences is related to indices solutions of:

%C x^k=Mod[a,n]

%D Burton, David M.,Elementary number theory,McGraw Hill,N.Y.,2002,pp173ff

%F t(n,k)=If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]

%e {1},

%e {1, 1},

%e {1, 1, 0},

%e {1, 1, 3, 1},

%e {1, 4, 27, 1, 0},

%e {1, 1, 3, 1, 5, 1},

%e {1, 4, 27, 256, 3125, 1, 0},

%e {1, 4, 27, 1, 5, 36, 343, 1},

%e {1, 4, 27, 256, 3125, 1, 7, 64, 0},

%e {1, 4, 27, 1, 5, 36, 343, 1, 9, 0}

%t t[n_, k_] = If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]

%t Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, 10}]]

%K nonn,tabf

%O 1,9

%A _Roger L. Bagula_, Nov 01 2009