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Search: id:A112599
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| A112599 |
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Triangle where a(1,1) = 1, a(n,m) = number of terms of row (n-1) which are coprime to m. |
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+0
5
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| 1, 1, 1, 2, 2, 2, 3, 0, 3, 0, 4, 2, 0, 2, 2, 5, 0, 4, 0, 4, 0, 6, 1, 3, 1, 2, 1, 3, 7, 5, 4, 5, 7, 3, 7, 5, 8, 7, 7, 7, 5, 6, 5, 7, 7, 9, 7, 8, 7, 7, 7, 4, 7, 8, 5, 10, 7, 9, 7, 9, 6, 5, 7, 9, 6, 10, 11, 7, 6, 7, 8, 4, 8, 7, 6, 6, 11, 4, 12, 5, 9, 5, 12, 5, 9, 5, 9, 5, 10, 5, 12, 13, 9, 7, 9, 6, 6, 13, 9, 7
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OFFSET
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1,4
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COMMENT
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GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.
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EXAMPLE
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Row 6 of the triangle is [5,0,4,0,4,0]. Among these terms there are 6 terms coprime to 1, 1 term coprime to 2, 3 terms coprime to 3, 1 term coprime to 4, 2 terms coprime to 5, 1 term coprime to 6, and 3 terms coprime to 7. So row 7 is [6,1,3,1,2,1,3].
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1 1
2 2 2
3 0 3 0
4 2 0 2 2
5 0 4 0 4 0
6 1 3 1 2 1 3
7 5 4 5 7 3 7 5
8 7 7 7 5 6 5 7 7
9 7 8 7 7 7 4 7 8 5
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MATHEMATICA
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f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length[p]; t = Table[ Sum[ If[GCD[p[[j]], n] == 1, 1, 0], {j, k}], {n, k + 1}]; Return[Append[l, t]]; ]; Flatten[Nest[f, {{1}}, 13]] (*Chandler*)
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CROSSREFS
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Adjacent sequences: A112596 A112597 A112598 this_sequence A112600 A112601 A112602
Sequence in context: A035307 A004481 A004489 this_sequence A106795 A071455 A139465
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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), Dec 21 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 24 2005
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