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A356718

T(n,k) is the total number of prime factors, counted with multiplicity, of k!*(n-k)!, for 0 <= k <= n. Triangle read by rows.

0, 0, 0, 1, 0, 1, 2, 1, 1, 2, 4, 2, 2, 2, 4, 5, 4, 3, 3, 4, 5, 7, 5, 5, 4, 5, 5, 7, 8, 7, 6, 6, 6, 6, 7, 8, 11, 8, 8, 7, 8, 7, 8, 8, 11, 13, 11, 9, 9, 9, 9, 9, 9, 11, 13, 15, 13, 12, 10, 11, 10, 11, 10, 12, 13, 15, 16, 15, 14, 13, 12, 12, 12

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OFFSET

0,7

COMMENTS

k!*(n-k)! is the denominator in binomial(n,k) = n!/(k!*(n-k)!) and all prime factors in the denominator cancel to leave an integer, so that T(n,k) = A022559(n) - A132896(n,k).

LINKS

Dario T. de Castro, Rows n = 0..140 of triangle, flattened

FORMULA

T(n,k) = bigomega(k!*(n-k)!), where 0 <= k <= n.

T(n,0) = T(n,n) = A022559(n).

EXAMPLE

Triangle begins:

n\k| 0 1 2 3 4 5 6 7

---+--------------------------------------

0 | 0

1 | 0, 0;

2 | 1, 0, 1;