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A100346
Number of compositions of n into divisors of n.
24
1, 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, 185493291001, 2
OFFSET
0,3
LINKS
FORMULA
Coefficient of x^n in expansion of 1/(1-Sum_{d divides n} x^d ).
MAPLE
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, 80), x, n), n=0..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=0..50); # Alois P. Heinz, Mar 28 2017
MATHEMATICA
a[n_] := SeriesCoefficient[1/(1-DivisorSum[n, x^#&]), {x, 0, n}]; Array[a, 50] (* Jean-François Alcover, Apr 06 2017 *)
CROSSREFS
Cf. A018818.
Sequence in context: A130674 A284839 A286376 * A359004 A306387 A308692
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Dec 29 2004
EXTENSIONS
More terms from Emeric Deutsch, Feb 16 2005
a(0)=1 prepended by Alois P. Heinz, Nov 08 2023
STATUS
approved