A081417 A000720 applied to Pascal-triangle: Pi[C(n,j)], j,0..n and n=0,1,2,...

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 3, 2, 0, 0, 3, 4, 4, 3, 0, 0, 3, 6, 8, 6, 3, 0, 0, 4, 8, 11, 11, 8, 4, 0, 0, 4, 9, 16, 19, 16, 9, 4, 0, 0, 4, 11, 23, 30, 30, 23, 11, 4, 0, 0, 4, 14, 30, 46, 54, 46, 30, 14, 4, 0, 0, 5, 16, 38, 66, 89, 89, 66, 38, 16, 5, 0, 0, 5, 18, 47, 94, 138, 157, 138, 94

Offset

0,8

Links

G. C. Greubel, Rows n = 0..50 of triangle, flattened

Example

Triangle begins:
  0;
  0, 0;
  0, 1, 0;
  0, 2, 2,  0;
  0, 2, 3,  2,  0;
  0, 3, 4,  4,  3,  0;
  0, 3, 6,  8,  6,  3, 0;
  0, 4, 8, 11, 11,  8, 4, 0;
  0, 4, 9, 16, 19, 16, 9, 4, 0;

Maple

with(numtheory); seq(seq(pi(binomial(n, k)), k = 0 .. n), n = 0 .. 12); # G. C. Greubel, Aug 14 2019

Mathematica

Flatten[Table[Table[PrimePi[Binomial[n, j]], {j, 0, n}], {n, 0, 15}], 1]

Prog

(PARI) T(n, k) = primepi(binomial(n, k));
for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Aug 14 2019
(Magma) [#PrimesUpTo(Binomial(n, k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Aug 14 2019
(Sage) [[prime_pi(binomial(n, k)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Aug 14 2019

Crossrefs

Cf. A000720.

Sequence in context: A344837 A031124 A063695 * A133388 A354643 A282516

Adjacent sequences: A081414 A081415 A081416 * A081418 A081419 A081420

Keyword

nonn,tabl

Author

Labos Elemer, Apr 02 2003

Status

approved