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%I #39 Nov 20 2019 03:24:44
%S 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,
%T 121,13,1,128,729,3125,2401,1331,169,17,1,256,2187,15625,16807,14641,
%U 2197,289,19,1,512,6561,78125,117649,161051,28561,4913,361,23,1,1024,19683,390625,823543,1771561,371293
%N 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.
%C If n = p - 1 where p is prime, then row n lists the numbers with p divisors.
%C The partial sums of column k give the column k of A319076.
%F T(n,k) = A000040(k)^n, n >= 0, k >= 1.
%e The corner of the square array is as follows:
%e A000079 A000244 A000351 A000420 A001020 A001022 A001026
%e A000012 1, 1, 1, 1, 1, 1, 1, ...
%e A000040 2, 3, 5, 7, 11, 13, 17, ...
%e A001248 4, 9, 25, 49, 121, 169, 289, ...
%e A030078 8, 27, 125, 343, 1331, 2197, 4913, ...
%e A030514 16, 81, 625, 2401, 14641, 28561, 83521, ...
%e A050997 32, 243, 3125, 16807, 161051, 371293, 1419857, ...
%e A030516 64, 729, 15625, 117649, 1771561, 4826809, 24137569, ...
%e A092759 128, 2187, 78125, 823543, 19487171, 62748517, 410338673, ...
%e A179645 256, 6561, 390625, 5764801, 214358881, 815730721, 6975757441, ...
%e ...
%o (PARI) T(n, k) = prime(k)^n;
%Y Rows 0-13: A000012, A000040, A001248, A030078, A030514, A050997, A030516, A092759, A179645, A179665, A030629, A079395, A030631, A138031.
%Y 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).
%Y Columns 1-15: A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.
%Y Main diagonal gives A093360.
%Y Second diagonal gives A062457.
%Y Third diagonal gives A197987.
%Y Removing the 1's we have A182944/ A182945.
%Y Cf. A006093, A319074, A319076.
%K nonn,tabl,easy
%O 0,2
%A _Omar E. Pol_, Sep 09 2018
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