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A100346
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Number of compositions of n into divisors of n.
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24
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1, 2, 2, 6, 2, 25, 2, 56, 20, 129, 2, 1628, 2, 742, 450, 5272, 2, 45316, 2, 83344, 3321, 29967, 2, 5105722, 572, 200390, 26426, 5469759, 2, 154004511, 2, 47350056, 226020, 9262157, 51886, 15140335650, 2, 63346598, 2044895, 14700095926, 2
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OFFSET
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1,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..2000
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FORMULA
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Coefficient of x^n in expansion of 1/(1-Sum_{d divides n} x^d ).
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MAPLE
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with(numtheory): G:=proc(n) local DV: DV:=divisors(n): 1/(1-sum(x^DV[j], j=1..tau(n))) end: seq(coeff(series(G(n), x=0, 80), x^n), n=1..44); # Emeric Deutsch, Feb 16 2005
# second Maple program:
a:= proc(n) option remember; local b, l;
l, b:= numtheory[divisors](n),
proc(m) option remember; `if`(m=0, 1,
add(`if`(j>m, 0, b(m-j)), j=l))
end; b(n)
end:
seq(a(n), n=1..50); # Alois P. Heinz, Mar 28 2017
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MATHEMATICA
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a[n_] := SeriesCoefficient[1/(1-DivisorSum[n, x^#&]), {x, 0, n}]; Array[a, 50] (* Jean-François Alcover, Apr 06 2017 *)
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CROSSREFS
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Cf. A018818.
Sequence in context: A130674 A284839 A286376 * A359004 A306387 A308692
Adjacent sequences: A100343 A100344 A100345 * A100347 A100348 A100349
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Dec 29 2004
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EXTENSIONS
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More terms from Emeric Deutsch, Feb 16 2005
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STATUS
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approved
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