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A102715
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Triangle read by rows: T(n,k) is phi(binomial(n,k)), where phi is Euler's totient function (0 <= k <= n).
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1
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1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 4, 4, 4, 4, 1, 1, 2, 8, 8, 8, 2, 1, 1, 6, 12, 24, 24, 12, 6, 1, 1, 4, 12, 24, 24, 24, 12, 4, 1, 1, 6, 12, 24, 36, 36, 24, 12, 6, 1, 1, 4, 24, 32, 48, 72, 48, 32, 24, 4, 1, 1, 10, 40, 80, 80, 120, 120, 80, 80, 40, 10, 1, 1, 4, 20, 80, 240, 240
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OFFSET
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0,8
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COMMENTS
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Row n contains n+1 terms. Row sums yield A064450.
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LINKS
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FORMULA
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EXAMPLE
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T(6,3)=8 because the positive integers relatively prime to binomial(6,3)=20 and not exceeding 20 are 1,3,7,9,11,13,17 and 19.
Triangle begins:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 2, 2, 1;
1, 4, 4, 4, 4, 1;
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MAPLE
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with(numtheory): T:=(n, k)->phi(binomial(n, k)): for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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MATHEMATICA
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Flatten[Table[EulerPhi[Binomial[n, k]], {n, 0, 12}, {k, 0, n}]] (* Vincenzo Librandi, May 01 2019 *)
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PROG
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(Magma) /* As triangle */ [[EulerPhi(Binomial(n, k)): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, May 01 2019
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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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