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A182944
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Square array A(i,j), i >= 1, j >= 1, of prime powers prime(i)^j, by descending antidiagonals.
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12
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2, 4, 3, 8, 9, 5, 16, 27, 25, 7, 32, 81, 125, 49, 11, 64, 243, 625, 343, 121, 13, 128, 729, 3125, 2401, 1331, 169, 17, 256, 2187, 15625, 16807, 14641, 2197, 289, 19, 512, 6561, 78125, 117649, 161051, 28561, 4913, 361, 23
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OFFSET
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1,1
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COMMENTS
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We alternatively refer to this sequence as a triangle T(.,.), with T(n,k) = A(k,n-k+1) = prime(k)^(n-k+1).
The monotonic ordering of this sequence, prefixed by 1, is A000961.
The joint-rank array of this sequence is A182869.
Main diagonal gives A062457. - Omar E. Pol, Sep 11 2018
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1..150, flattened)
Michael De Vlieger, Diagram 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.
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FORMULA
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From Peter Munn, Dec 29 2019: (Start)
A(i,j) = A182945(j,i) = A319075(j,i).
A(i,j) = A242378(i-1,2^j) = A329332(2^(i-1),j).
A(i,i) = A062457(i).
(End)
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EXAMPLE
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Square array A(i,j) begins:
i \ j: 1 2 3 4 5 ...
---\-------------------------------------
1: 2, 4, 8, 16, 32, ...
2: 3, 9, 27, 81, 243, ...
3: 5, 25, 125, 625, 3125, ...
4: 7, 49, 343, 2401, 16807, ...
...
The triangle T(n,k) begins:
n\k: 1 2 3 4 5 6 ...
1: 2
2: 4 3
3: 8 9 5
4: 16 27 25 7
5: 32 81 125 49 11
6: 64 243 625 343 121 13
...
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MATHEMATICA
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TableForm[Table[Prime[n]^j, {n, 1, 14}, {j, 1, 8}]]
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CROSSREFS
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Cf. A000961, A006939 (row products of triangle), A062457, A182945, A332979 (row maxima of triangle).
Columns: A000040 (1), A001248 (2), A030078 (3), A030514 (4), A050997 (5), A030516 (6), A092759 (7), A179645 (8), A179665 (9), A030629 (10).
A319075 extends the array with 0th powers.
Subtable of A242378, A284457, A329332.
Sequence in context: A048767 A269851 A284457 * A269385 A252755 A163511
Adjacent sequences: A182941 A182942 A182943 * A182945 A182946 A182947
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Dec 14 2010
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EXTENSIONS
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Clarified in respect of alternate reading as a triangle by Peter Munn, Aug 28 2022
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STATUS
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approved
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