cp's OEIS Frontend

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.

%I A319075 #39 Nov 20 2019 03:24:44
%S A319075 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 A319075 121,13,1,128,729,3125,2401,1331,169,17,1,256,2187,15625,16807,14641,
%U A319075 2197,289,19,1,512,6561,78125,117649,161051,28561,4913,361,23,1,1024,19683,390625,823543,1771561,371293
%N 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.
%C A319075 If n = p - 1 where p is prime, then row n lists the numbers with p divisors.
%C A319075 The partial sums of column k give the column k of A319076.
%F A319075 T(n,k) = A000040(k)^n, n >= 0, k >= 1.
%e A319075 The corner of the square array is as follows:
%e A319075          A000079 A000244 A000351  A000420    A001020    A001022     A001026
%e A319075 A000012        1,      1,      1,       1,         1,         1,          1, ...
%e A319075 A000040        2,      3,      5,       7,        11,        13,         17, ...
%e A319075 A001248        4,      9,     25,      49,       121,       169,        289, ...
%e A319075 A030078        8,     27,    125,     343,      1331,      2197,       4913, ...
%e A319075 A030514       16,     81,    625,    2401,     14641,     28561,      83521, ...
%e A319075 A050997       32,    243,   3125,   16807,    161051,    371293,    1419857, ...
%e A319075 A030516       64,    729,  15625,  117649,   1771561,   4826809,   24137569, ...
%e A319075 A092759      128,   2187,  78125,  823543,  19487171,  62748517,  410338673, ...
%e A319075 A179645      256,   6561, 390625, 5764801, 214358881, 815730721, 6975757441, ...
%e A319075 ...
%o A319075 (PARI) T(n, k) = prime(k)^n;
%Y A319075 Rows 0-13: A000012, A000040, A001248, A030078, A030514, A050997, A030516, A092759, A179645, A179665, A030629, A079395, A030631, A138031.
%Y A319075 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 A319075 Columns 1-15: A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.
%Y A319075 Main diagonal gives A093360.
%Y A319075 Second diagonal gives A062457.
%Y A319075 Third diagonal gives A197987.
%Y A319075 Removing the 1's we have A182944/ A182945.
%Y A319075 Cf. A006093, A319074, A319076.
%K A319075 nonn,tabl,easy
%O A319075 0,2
%A A319075 _Omar E. Pol_, Sep 09 2018