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A119586
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Triangle where T(n,m) = (n+1-m)-th positive integer with (m+1) divisors.
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2
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2, 3, 4, 5, 9, 6, 7, 25, 8, 16, 11, 49, 10, 81, 12, 13, 121, 14, 625, 18, 64, 17, 169, 15, 2401, 20, 729, 24, 19, 289, 21, 14641, 28, 15625, 30, 36, 23, 361, 22, 28561, 32, 117649, 40, 100, 48, 29, 529, 26, 83521, 44, 1771561, 42, 196, 80, 1024, 31, 841, 27
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OFFSET
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1,1
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COMMENTS
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As a square array A(n,m), n, m >= 1, read by ascending antidiagonals, A(n,m) is the n-th positive integer with m+1 divisors.
Thus both formats list the numbers with m+1 divisors in their m-th column. For the corresponding sequences giving numbers with a specific number of divisors see the index entries link.
(End)
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LINKS
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EXAMPLE
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Looking at the 4th row, 7 is the 4th positive integer with 2 divisors, 25 is the 3rd positive integer with 3 divisors, 8 is the 2nd positive integer with 4 divisors and 16 is the first positive integer with 5 divisors. So the 4th row is (7,25,8,16).
The triangle T(n,m) begins:
n\m: 1 2 3 4 5 6 7
---------------------------------------------
1 : 2
2 : 3 4
3 : 5 9 6
4 : 7 25 8 16
5 : 11 49 10 81 12
6 : 13 121 14 625 18 64
7 : 17 169 15 2401 20 729 24
...
Square array A(n,m) begins:
n\m: 1 2 3 4 5 ...
--------------------------------------------
1 : 2 4 6 16 12 ...
2 : 3 9 8 81 18 ...
3 : 5 25 10 625 20 ...
4 : 7 49 14 2401 28 ...
5 : 11 121 15 14641 32 ...
...
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MATHEMATICA
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t[n_, m_] := Block[{c = 0, k = 1}, While[c < n + 1 - m, k++; If[DivisorSigma[0, k] == m + 1, c++ ]]; k]; Table[ t[n, m], {n, 11}, {m, n}] // Flatten (* Robert G. Wilson v, Jun 07 2006 *)
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CROSSREFS
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Diagonals (equivalently, rows of the square array) start: A005179\{1}, A161574.
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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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