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A085604 T(n,k) = highest power of prime(k) dividing n!, read by rows. 7
0, 1, 0, 1, 1, 0, 3, 1, 0, 0, 3, 1, 1, 0, 0, 4, 2, 1, 0, 0, 0, 4, 2, 1, 1, 0, 0, 0, 7, 2, 1, 1, 0, 0, 0, 0, 7, 4, 1, 1, 0, 0, 0, 0, 0, 8, 4, 2, 1, 0, 0, 0, 0, 0, 0, 8, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 10, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 10, 5, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 11, 5, 2, 2, 1, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

T(n,1) = A011371(n); T(n,2) = A054861(n) for n>1;

T(n,k) = number of occurrences of prime(k) as factor in numbers <= n (with repetitions);

Sum{T(n,k): 1<=k<=n} = A022559(n);

T(n, A000720(n)) = 1; T(n,k) = 0, A000720(n)<k<n.

T(n,k) = A115627(n,k) for n > 1 and k=1..A000720(n). - Reinhard Zumkeller, Nov 01 2013

LINKS

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

EXAMPLE

0;

1,0;

1,1,0;

3,1,0,0;

3,1,1,0,0;

4,2,1,0,0,0;

4,2,1,1,0,0,0;

7,2,1,1,0,0,0,0;

7,4,1,1,0,0,0,0,0;

8,4,2,1,0,0,0,0,0,0;

PROG

(Haskell)

a085604 n k = a085604_tabl !! (n-2) !! (k-1)

a085604_row 1 = [0]

a085604_row n = a115627_row n ++ (take $ a062298 $ fromIntegral n) [0, 0..]

a085604_tabl = map a085604_row [1..]

-- Reinhard Zumkeller, Nov 01 2013

CROSSREFS

Cf. A141809, A115627, A000142.

Sequence in context: A027200 A035654 A170846 * A306268 A144357 A122848

Adjacent sequences:  A085601 A085602 A085603 * A085605 A085606 A085607

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Jul 07 2003

STATUS

approved

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Last modified August 20 18:11 EDT 2019. Contains 326154 sequences. (Running on oeis4.)