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A083140
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Sieve of Eratosthenes arranged as an array and read by antidiagonals in the up direction; n-th row has property that smallest prime factor is prime(n).
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48
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2, 3, 4, 5, 9, 6, 7, 25, 15, 8, 11, 49, 35, 21, 10, 13, 121, 77, 55, 27, 12, 17, 169, 143, 91, 65, 33, 14, 19, 289, 221, 187, 119, 85, 39, 16, 23, 361, 323, 247, 209, 133, 95, 45, 18, 29, 529, 437, 391, 299, 253, 161, 115, 51, 20, 31, 841, 667, 551, 493, 377, 319, 203, 125, 57, 22
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OFFSET
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2,1
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COMMENTS
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A permutation of natural numbers >= 2.
The proportion of the integers after the n-th row of the array is given by A005867(n)/A002110(n). - Tom Hanlon, Jun 08 2019
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LINKS
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EXAMPLE
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Array begins:
2 4 6 8 10 12 14 16 18 20 22 24 .... (A005843 \ {0})
3 9 15 21 27 33 39 45 51 57 63 69 .... (A016945)
5 25 35 55 65 85 95 115 125 145 155 175 .... (A084967)
7 49 77 91 119 133 161 203 217 259 287 301 .... (A084968)
11 121 143 187 209 253 319 341 407 451 473 517 .... (A084969)
13 169 221 247 299 377 403 481 533 559 611 689 .... (A084970)
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MATHEMATICA
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a = Join[ {Table[2n, {n, 1, 12}]}, Table[ Take[ Prime[n]*Select[ Range[100], GCD[ Prime[n] #, Product[ Prime[i], {i, 1, n - 1}]] == 1 &], 12], {n, 2, 12}]]; Flatten[ Table[ a[[i, n - i]], {n, 2, 12}, {i, n - 1, 1, -1}]]
(* second program: *)
rows = 12; Clear[T]; Do[For[m = p = Prime[n]; k = 1, k <= rows, m += p, If[ FactorInteger[m][[1, 1]] == p, T[n, k++] = m]], {n, rows}]; Table[T[n - k + 1, k], {n, rows}, {k, n}] // Flatten (* Jean-François Alcover, Mar 08 2016 *)
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CROSSREFS
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Arrays of integers grouped into rows by various criteria:
by lowest prime factor: this sequence (upward antidiagonals), A083221 (downward antidiagonals),
by number of distinct prime factors: A125666,
by number of prime factors counted with multiplicity: A078840,
by ordered prime signature: A096153,
by number of 1's in binary expansion: A066884 (upward), A067576 (downward),
by distance to next prime: A192179.
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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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