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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If n = p - 1 where p is prime, then row n lists the numbers with p divisors.

The partial sums of column k give the column k of A319076.

LINKS

Table of n, a(n) for n=0..60.

FORMULA

T(n,k) = A000040(k)^n, n >= 0, k >= 1.

EXAMPLE

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, ...

...

PROG

(PARI) T(n, k) = prime(k)^n;

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.

Removing the 1's we have A182944/ A182945.

Cf. A006093, A319074, A319076.

Sequence in context: A106195 A247023 A051129 * A264871 A067410 A213947

Adjacent sequences:  A319072 A319073 A319074 * A319076 A319077 A319078

KEYWORD

nonn,tabl,easy

AUTHOR

Omar E. Pol, Sep 09 2018

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)