A120458 Triangle read by rows: row 0 is 1; for n>0, row n gives 1^n, prime(1)^n, prime(2)^n, ..., prime(n)^n.

1, 1, 2, 1, 4, 9, 1, 8, 27, 125, 1, 16, 81, 625, 2401, 1, 32, 243, 3125, 16807, 161051, 1, 64, 729, 15625, 117649, 1771561, 4826809, 1, 128, 2187, 78125, 823543, 19487171, 62748517, 410338673, 1, 256, 6561, 390625, 5764801, 214358881, 815730721

Offset

0,3

Comments

Polynomials like x^2+2^2*x+3^2 and x^4+2^4+x^3+3^4*x^2+5^4*x+7^4 inspired this sequence.

Links

Table of n, a(n) for n=0..42.

Example

1
1, 2
1, 4, 9
1, 8, 27, 125
1, 16, 81, 625, 2401
1, 32, 243, 3125, 16807, 161051

Mathematica

T[n_, m_] := If[n == 0, 1, Prime[n]^m] a = Table[Table[T[n, m], {n, 0, m}], {m, 0, 10}] b = Flatten[a] MatrixForm[a]
Module[{nn=10, pr}, pr=Prime[Range[nn]]; Flatten[Table[Join[{1}, Take[pr, n]^n], {n, 0, nn}]]] (* Harvey P. Dale, Sep 26 2014 *)

Crossrefs

Rows n=1, 2, 3, .., 7 are A000040, A001248, A030078, A030514, A050997, A030516 and A092759. - R. J. Mathar, Mar 23 2007

Sequence in context: A182739 A359132 A076014 * A183244 A086933 A077878

Adjacent sequences: A120455 A120456 A120457 * A120459 A120460 A120461

Keyword

nonn,tabl

Author

Roger L. Bagula, Jun 24 2006

Extensions

Edited by N. J. A. Sloane, Mar 26 2007

Status

approved