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A132896
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Triangle read by rows: T(n,k)=number of prime divisors of C(n,k), counted with multiplicity (0<=k<=n).
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2
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 3, 2, 2, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 3, 3, 4, 3, 4, 3, 3, 0, 0, 2, 4, 4, 4, 4, 4, 4, 2, 0, 0, 2, 3, 5, 4, 5, 4, 5, 3, 2, 0, 0, 1, 2, 3, 4, 4, 4, 4, 3, 2, 1, 0, 0, 3, 3, 4, 4, 6, 5, 6, 4, 4, 3, 3, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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LINKS
| T. D. Noe, Rows n=0..100 of triangle, flattened
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EXAMPLE
| T(8,3)=4 because C(8,3)=56=2*2*2*7.
Triangle begins:
0;
0,0;
0,1,0;
0,1,1,0;
0,2,2,2,0;
0,1,2,2,1,0;
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MAPLE
| with(numtheory): T:=proc(n, k) if k <= n then bigomega(binomial(n, k)) else x end if end proc: for n from 0 to 12 do seq(T(n, k), k=0..n) end do; # yields sequence in triangular form
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CROSSREFS
| Cf. A048571, which counts only distinct factors.
Sequence in context: A039967 A123186 A127323 * A089789 A004541 A178045
Adjacent sequences: A132893 A132894 A132895 * A132897 A132898 A132899
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 16 2007
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