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%I #52 Jul 18 2023 07:37:57
%S 2,4,3,8,9,5,16,27,25,7,32,81,125,49,11,64,243,625,343,121,13,128,729,
%T 3125,2401,1331,169,17,256,2187,15625,16807,14641,2197,289,19,512,
%U 6561,78125,117649,161051,28561,4913,361,23
%N Square array A(i,j), i >= 1, j >= 1, of prime powers prime(i)^j, by descending antidiagonals.
%C We alternatively refer to this sequence as a triangle T(.,.), with T(n,k) = A(k,n-k+1) = prime(k)^(n-k+1).
%C The monotonic ordering of this sequence, prefixed by 1, is A000961.
%C The joint-rank array of this sequence is A182869.
%C Main diagonal gives A062457. - _Omar E. Pol_, Sep 11 2018
%H Michael De Vlieger, <a href="/A182944/b182944.txt">Table of n, a(n) for n = 1..11325</a> (rows 1..150, flattened)
%H Michael De Vlieger, <a href="/A182944/a182944.png">Diagram</a> showing row n of triangle in a semicircle as noted, with a color function associated with the magnitude of T(n,k) compared to 2^n in light blue, where prime(n) is the smallest and the prime power indicated in red the largest in the row.
%F From _Peter Munn_, Dec 29 2019: (Start)
%F A(i,j) = A182945(j,i) = A319075(j,i).
%F A(i,j) = A242378(i-1,2^j) = A329332(2^(i-1),j).
%F A(i,i) = A062457(i).
%F (End)
%e Square array A(i,j) begins:
%e i \ j: 1 2 3 4 5 ...
%e ---\-------------------------------------
%e 1: 2, 4, 8, 16, 32, ...
%e 2: 3, 9, 27, 81, 243, ...
%e 3: 5, 25, 125, 625, 3125, ...
%e 4: 7, 49, 343, 2401, 16807, ...
%e ...
%e The triangle T(n,k) begins:
%e n\k: 1 2 3 4 5 6 ...
%e 1: 2
%e 2: 4 3
%e 3: 8 9 5
%e 4: 16 27 25 7
%e 5: 32 81 125 49 11
%e 6: 64 243 625 343 121 13
%e ...
%t TableForm[Table[Prime[n]^j,{n,1,14},{j,1,8}]]
%Y Cf. A000961, A006939 (row products of triangle), A062457, A182945, A332979 (row maxima of triangle).
%Y Columns: A000040 (1), A001248 (2), A030078 (3), A030514 (4), A050997 (5), A030516 (6), A092759 (7), A179645 (8), A179665 (9), A030629 (10).
%Y A319075 extends the array with 0th powers.
%Y Subtable of A242378, A284457, A329332.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Dec 14 2010
%E Clarified in respect of alternate reading as a triangle by _Peter Munn_, Aug 28 2022
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