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A081417
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A000720 applied to Pascal-triangle: Pi[C(n,j)], j,0..n and n=0,1,2,...
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2
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,8
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LINKS
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EXAMPLE
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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;
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MAPLE
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with(numtheory); seq(seq(pi(binomial(n, k)), k = 0 .. n), n = 0 .. 12); # G. C. Greubel, Aug 14 2019
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MATHEMATICA
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Flatten[Table[Table[PrimePi[Binomial[n, j]], {j, 0, n}], {n, 0, 15}], 1]
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PROG
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(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
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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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