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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) 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.)