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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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8
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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This sequence is a permutation of the integers >= 2.
Since the table has been entered by rising instead of falling antidiagonals, the sequence represents the transpose, with columns instead of rows: cf. the "table" link, section "infinite square array". - M. F. Hasler, Oct 22 2019
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LINKS
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EXAMPLE
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Array begins: (rows here appear as columns in the "table" display of the sequence)
2, 4, 8, 16, 32, 64, 128, 256, 512, ... (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. That is, 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 (* Ray Chandler, Feb 09 2007 *)
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PROG
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(PARI) T=List(); r=c=1; for(n=1, 99, #T<r && listput(T, List(prime(r))); #T[r]<c && listput(T[r], T[r][c-1]) && while(vecmax(factor(T[r][c]+=T[r][1])[, 1])>T[r][1], ); print1(T[r][c]", "); r-- && c++ || r=c+c=1) \\ M. F. Hasler, Oct 22 2019
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CROSSREFS
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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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