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Search: id:A123175
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| A123175 |
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Table (read by antidiagonals) where t(0,0)=1, t(m,n) = number of terms above and to the left of t(m,n) (i.e. number of t(k,j)'s, where 0<=k<=m, 0<=j<=n, excluding the t(m,n) case itself) which are coprime to (m+n). |
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+0
1
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| 1, 1, 1, 2, 3, 2, 3, 4, 4, 3, 3, 5, 4, 5, 3, 5, 8, 10, 10, 8, 5, 3, 5, 4, 5, 4, 5, 3, 7, 13, 17, 19, 19, 17, 13, 7, 7, 12, 12, 14, 13, 14, 12, 12, 7, 6, 12, 17, 21, 24, 24, 21, 17, 12, 6, 7, 10, 12, 14, 15, 13, 15, 14, 12, 10, 7, 11, 21, 29, 35, 39, 41, 41, 39, 35, 29, 21, 11, 7, 11, 13
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OFFSET
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0,4
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EXAMPLE
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The first 4 columns and first 6 rows (excluding t(5,3)) of the table is:
1,1,2,3
1,3,4,5
2,4,4,10
3,5,10,5
3,8,4,19
5,5,17,
The number of these terms which are coprime to (5+3) is 14 (the odd terms). So t(5, 3) = 14.
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MATHEMATICA
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t[0, 0] = 1; t[m_, n_] := t[m, n] = Block[{c = 0}, Do[ Do[ If[k == m && j == n, Continue[]]; If[GCD[t[k, j], m + n] == 1, c++ ]; , {j, 0, n}]; , {k, 0, m}]; c]; Flatten[Table[t[d - i, i], {d, 0, 12}, {i, 0, d}]] (*Chandler*)
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CROSSREFS
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Adjacent sequences: A123172 A123173 A123174 this_sequence A123176 A123177 A123178
Sequence in context: A124524 A124525 A106788 this_sequence A143998 A054237 A129600
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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), Nov 04 2006
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 11 2006
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