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A279394
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Triangle read by rows, T(n,m) = sigma_{n-m}(m) for n >= 1, m = 1,2, ..., n.
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11
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1, 1, 2, 1, 3, 2, 1, 5, 4, 3, 1, 9, 10, 7, 2, 1, 17, 28, 21, 6, 4, 1, 33, 82, 73, 26, 12, 2, 1, 65, 244, 273, 126, 50, 8, 4, 1, 129, 730, 1057, 626, 252, 50, 15, 3, 1, 257, 2188, 4161, 3126, 1394, 344, 85, 13, 4, 1, 513, 6562, 16513, 15626, 8052, 2402, 585, 91, 18, 2, 1, 1025, 19684, 65793, 78126, 47450, 16808, 4369, 757, 130, 12, 6
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OFFSET
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1,3
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COMMENTS
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See A109974 (downward antidiagonals) for details and references. sigma_k(n) is the sum of the k-th power of the positive divisors of n.
This is the triangle read by rows obtained from the array sigma_k(n) for k >= 0, n >= 1, read by upward antidiagonals.
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LINKS
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FORMULA
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T(n, m) = sigma_{n-m}(m), n >= 1, m = 1..n.
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EXAMPLE
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The triangle T(n, m) begins:
n\m 1 2 3 4 5 6 7 8 9 10
1: 1
2: 1 2
3: 1 3 2
4: 1 5 4 3
5: 1 9 10 7 2
6: 1 17 28 21 6 4
7: 1 33 82 73 26 12 2
8: 1 65 244 273 126 50 8 4
9: 1 129 730 1057 626 252 50 15 3
10: 1 257 2188 4161 3126 1394 344 85 13 4
...
n = 11: 1 513 6562 16513 15626 8052 2402 585 91 18 2,
n = 12: 1 1025 19684 65793 78126 47450 16808 4369 757 130 12 6.
...
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MAPLE
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T := (n, k) -> numtheory:-sigma[n-k](k):
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MATHEMATICA
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Table[DivisorSigma[k, #] &[n - k + 1], {n, 0, 11}, {k, n, 0, -1}] (* Michael De Vlieger, Jan 09 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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