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Search: id:A125624
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| A125624 |
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Array read by antidiagonals: n-th row contains the positive integers with their largest prime factor equal to the n-th prime. |
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+0
1
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| 2, 3, 4, 5, 6, 8, 7, 10, 9, 16, 11, 14, 15, 12, 32, 13, 22, 21, 20, 18, 64, 17, 26, 33, 28, 25, 24, 128, 19, 34, 39, 44, 35, 30, 27, 256, 23, 38, 51, 52, 55, 42, 40, 36, 512, 29, 46, 57, 68, 65, 66, 49, 45, 48, 1024, 31, 58, 69, 76, 85, 78, 77, 56, 50, 54, 2048, 37, 62, 87, 92
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence is a permutation of the integers >= 2.
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EXAMPLE
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Array begins:
2,4,8,16,32,64,128,256,...(A000079)
3,6,9,12,18,24,27,36,48,...(A065119)
5,10,15,20,25,30,40,45,50,...(A080193)
7,14,21,28,35,42,49,56,63,...(A080194)
11,22,33,44,55,66,77,88,99,...(A080195)
13,26,39,52,65,78,91,104,117,...(A080196)
The 3rd row, for example, contains the positive integers where the 3rd prime, 5, is the largest prime divisor. ie Each integer in this row is divisible by 5, and may be divisible by 2 or 3 as well, but none of the integers in this row are divisible by primes larger than 5. (So for example, 35 = 5*7 is excluded from the 3rd row.)
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MATHEMATICA
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lpf[n_] := FactorInteger[n][[ -1, 1]]; f[n_, m_] := f[n, m] = Block[{k}, k = If[m == 1, Prime[n], f[n, m - 1] + 1]; While[lpf[k] != Prime[n], k++ ]; k]; Table[f[ d - m + 1, m], {d, 12}, {m, d}] // Flatten(*Chandler*)
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CROSSREFS
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Cf. A083140, A006530, A000040 (1st col), A033286 (main diag), A077320.
Sequence in context: A078840 A129129 A114622 this_sequence A003965 A097502 A064364
Adjacent sequences: A125621 A125622 A125623 this_sequence A125625 A125626 A125627
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KEYWORD
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nonn,tabl
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Jan 27 2007
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 09 2007
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