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A033630
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Number of partitions of n into distinct divisors of n.
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68
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1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 8, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 4, 1, 3, 1, 1, 1, 35, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 2, 1, 7, 1, 1, 1, 26, 1, 1, 1, 2, 1, 24, 1, 1, 1, 1, 1, 22, 1, 1, 1, 3
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OFFSET
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0,7
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LINKS
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FORMULA
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a(n) = f(n, n, 1) with f(n, m, k) = if k <= m then f(n, m, k + 1) + f(n, m - k, k + 1)*0^(n mod k) else 0^m. - Reinhard Zumkeller, Dec 11 2009
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EXAMPLE
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a(12) = 3 because we have the partitions [12], [6, 4, 2], and [6, 3, 2, 1].
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MAPLE
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with(numtheory): a:=proc(n) local div, g, gser: div:=divisors(n): g:=product(1+x^div[j], j=1..tau(n)): gser:=series(g, x=0, 105): coeff(gser, x^n): end: seq(a(n), n=1..100); # Emeric Deutsch, Mar 30 2006
# second Maple program:
with(numtheory):
a:= proc(n) local b, l; l:= sort([(divisors(n))[]]):
b:= proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,
b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i-1))))
end; forget(b):
b(n, nops(l))
end:
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MATHEMATICA
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A033630 = Table[SeriesCoefficient[Series[Times@@((1 + z^#) & /@ Divisors[n]), {z, 0, n}], n ], {n, 512}] (* Wouter Meeussen *)
A033630[n_] := f[n, n, 1]; f[n_, m_, k_] := f[n, m, k] = If[k <= m, f[n, m, k + 1] + f[n, m - k, k + 1] * Boole[Mod[n, k] == 0], Boole[m == 0]]; Array[A033630, 101, 0] (* Jean-François Alcover, Jul 29 2015, after Reinhard Zumkeller *)
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PROG
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(Haskell)
a033630 0 = 1
a033630 n = p (a027750_row n) n where
p _ 0 = 1
p [] _ = 0
p (d:ds) m = if d > m then 0 else p ds (m - d) + p ds m
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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