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A090622
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Square array read by antidiagonals of highest power of k dividing n! (with n,k>1).
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11
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1, 0, 1, 0, 1, 3, 0, 0, 1, 3, 0, 0, 1, 1, 4, 0, 1, 0, 1, 2, 4, 0, 0, 1, 1, 2, 2, 7, 0, 0, 0, 1, 1, 2, 2, 7, 0, 0, 1, 0, 2, 1, 3, 4, 8, 0, 0, 0, 1, 0, 2, 1, 3, 4, 8, 0, 0, 0, 0, 1, 1, 2, 1, 4, 4, 10, 0, 0, 0, 1, 1, 1, 1, 4, 1, 4, 5, 10, 0, 0, 1, 0, 1, 1, 2, 1, 4, 1, 5, 5, 11, 0, 0, 0, 1, 0, 1, 1, 2, 1, 4, 1, 5, 5
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,6
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FORMULA
| For k=p prime: T(n, p)=[n/p]+[n/p^2]+[n/p^3]+.... For k=p^m a prime power: T(n, p^m)=[T(n, p)/m]. For k=b*c with b and c coprime: T(n, a*b)=min(T(n, a), T(n, b)). T(n, k) is close to, but below, n/A090624(k).
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EXAMPLE
| Rows start: 1,0,0,0,0,...; 1,1,0,0,1,...; 3,1,1,0,1,...; 3,1,1,1,1,...; 4,2,2,1,2,...; 4,2,2,1,2,...; 7,2,3,1,2,...; etc.
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CROSSREFS
| Columns include A011371, A054861, A090616, A027868, A054861, A054896, A090617, A090618, A027868, A064458, A090619, A090620, A054896, A027868, A090621. Cf. A090623, A090624.
Cf. A115627.
Sequence in context: A151859 A163541 A165974 * A035696 A170840 A035630
Adjacent sequences: A090619 A090620 A090621 * A090623 A090624 A090625
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Dec 06 2003
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