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Search: id:A066032
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| A066032 |
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Number of ways to write n as a product with no factor larger than m (1 <= m <=n, written row by row). |
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+0
2
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| 1, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 2, 3, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2
(list; table; graph; listen)
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OFFSET
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1,10
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FORMULA
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T(1, 1) = 1. For every prime p T(p, m) = 1 if p <= m and 0 else. For composite n: T(n, m) = sum[T(n/d, d)] + I(n<=m) where the sum is over all divisors d of n except 1 and n with d <= m and I(n<=m) is 1 if n<=m and 0 else.
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EXAMPLE
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T(12, 5) = a(71) = 2, since there are 2 possibilities to write 12 as a product with no factor larger than 5 (4*3 and 3*2*2)
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MAPLE
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with(numtheory): T := proc(n::integer, m::integer) local i, A, summe, d: if isprime(n) then: if n <= m then RETURN(1) fi: RETURN(0): fi:
A := divisors(n) minus {n, 1}: for d in A do: if d > m then A := A minus {d}: fi: od: summe := 0: for d in A do: summe := summe + T(n/d, d): od: if n <=m then summe := summe + 1: fi: RETURN(summe): end: A066032 := [seq(seq(T(n, m), m=1..n), n=1..16)];
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CROSSREFS
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A001055(n) = T(n, n) is the right diagonal.
Sequence in context: A127475 A086014 A025437 this_sequence A035187 A033770 A101668
Adjacent sequences: A066029 A066030 A066031 this_sequence A066033 A066034 A066035
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KEYWORD
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nonn,tabl
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com), Feb 11 2002
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