A167284 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]]]

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

Offset

1,9

Comments

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]

References

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

Links

Table of n, a(n) for n=1..54.

Formula

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

Example

{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}

Mathematica

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}]]

Crossrefs

Sequence in context: A346792 A294316 A294761 * A016463 A155727 A098084

Adjacent sequences: A167281 A167282 A167283 * A167285 A167286 A167287

Keyword

nonn,tabf

Author

Roger L. Bagula, Nov 01 2009

Status

approved