A102715 Triangle read by rows: T(n,k) is phi(binomial(n,k)), where phi is Euler's totient function (0 <= k <= n).
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
Offset: 0
Examples
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;
Programs
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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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Maple
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
Flatten[Table[EulerPhi[Binomial[n, k]], {n, 0, 12}, {k, 0, n}]] (* Vincenzo Librandi, May 01 2019 *)
Comments