A319075 Square array T(n,k) read by antidiagonal upwards in which row n lists the n-th powers of primes, hence column k lists the powers of the k-th prime, n >= 0, k >= 1.
1, 2, 1, 4, 3, 1, 8, 9, 5, 1, 16, 27, 25, 7, 1, 32, 81, 125, 49, 11, 1, 64, 243, 625, 343, 121, 13, 1, 128, 729, 3125, 2401, 1331, 169, 17, 1, 256, 2187, 15625, 16807, 14641, 2197, 289, 19, 1, 512, 6561, 78125, 117649, 161051, 28561, 4913, 361, 23, 1, 1024, 19683, 390625, 823543, 1771561, 371293
Offset: 0
Examples
The corner of the square array is as follows:
A000079 A000244 A000351 A000420 A001020 A001022 A001026
A000012 1, 1, 1, 1, 1, 1, 1, ...
A000040 2, 3, 5, 7, 11, 13, 17, ...
A001248 4, 9, 25, 49, 121, 169, 289, ...
A030078 8, 27, 125, 343, 1331, 2197, 4913, ...
A030514 16, 81, 625, 2401, 14641, 28561, 83521, ...
A050997 32, 243, 3125, 16807, 161051, 371293, 1419857, ...
A030516 64, 729, 15625, 117649, 1771561, 4826809, 24137569, ...
A092759 128, 2187, 78125, 823543, 19487171, 62748517, 410338673, ...
A179645 256, 6561, 390625, 5764801, 214358881, 815730721, 6975757441, ...
...
Crossrefs
Rows 0-13: A000012, A000040, A001248, A030078, A030514, A050997, A030516, A092759, A179645, A179665, A030629, A079395, A030631, A138031.
Other rows n: A030635 (n=16), A030637 (n=18), A137486 (n=22), A137492 (n=28), A139571 (n=30), A139572 (n=36), A139573 (n=40), A139574 (n=42), A139575 (n=46), A173533 (n=52), A183062 (n=58), A183085 (n=60), A261700 (n=100).
Columns 1-15: A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.
Main diagonal gives A093360.
Second diagonal gives A062457.
Third diagonal gives A197987.
Programs
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PARI
T(n, k) = prime(k)^n;
Formula
T(n,k) = A000040(k)^n, n >= 0, k >= 1.
Comments