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A167284
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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]]]
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0
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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, 27, 1, 5, 36, 343, 1, 1, 4, 27, 256, 3125, 1, 7, 64, 0, 1, 4, 27, 1, 5, 36, 343, 1, 9
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OFFSET
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1,9
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COMMENTS
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Row sums are:
{1, 2, 2, 6, 33, 12, 3414, 418, 3485, 427,...}
The sequences is related to indices solutions of:
x^k=Mod[a,n]
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REFERENCES
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Burton, David M.,Elementary number theory,McGraw Hill,N.Y.,2002,pp173ff
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LINKS
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FORMULA
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t(n,k)=If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]
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EXAMPLE
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{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, 27, 1, 5, 36, 343, 1},
{1, 4, 27, 256, 3125, 1, 7, 64, 0},
{1, 4, 27, 1, 5, 36, 343, 1, 9, 0}
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MATHEMATICA
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t[n_, k_] = If[Mod[k, n] == 0 && (Mod[k, EulerPhi[n]] == 0), 1, Mod[k, n] ^ Mod[k, EulerPhi[n]]]
Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, 10}]]
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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