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A096153
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Natural numbers (greater than 1) arranged in rows according to their ordered prime signature. Square array A(n,k) read by descending antidiagonals.
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1
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2, 3, 4, 5, 9, 6, 7, 25, 10, 8, 11, 49, 14, 27, 12, 13, 121, 15, 125, 20, 16, 17, 169, 21, 343, 28, 81, 18, 19, 289, 22, 1331, 44, 625, 50, 24, 23, 361, 26, 2197, 45, 2401, 75, 40, 30, 29, 529, 33, 4913, 52, 14641, 98, 56, 42, 32, 31, 841, 34, 6859, 63, 28561, 147, 88, 66
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OFFSET
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1,1
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COMMENTS
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The first row is A000040 (the prime numbers) and the first column is A055932 (the Quet prime signatures).
If we restrict the terms to those having ordered prime signatures that are not represented in A025487 (the least prime signature sequence), we get A096011.
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LINKS
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EXAMPLE
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18 = 2^1 * 3^2, so has ordered prime signature (1,2) given by the exponents in the factorization shown. No earlier number has this prime signature, so 18 is placed at the start of the next empty row (row 7). Thus A(7,1) = 18.
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CROSSREFS
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For m >= 2, A077462/A335286 essentially give the row/column containing m.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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