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A100346 Number of compositions of n into divisors of n. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..2000

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=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

MATHEMATICA

a[n_] := SeriesCoefficient[1/(1-DivisorSum[n, x^#&]), {x, 0, n}]; Array[a, 50] (* Jean-Fran├žois Alcover, Apr 06 2017 *)

CROSSREFS

Cf. A018818.

Sequence in context: A130674 A284839 A286376 * A306387 A308692 A319352

Adjacent sequences:  A100343 A100344 A100345 * A100347 A100348 A100349

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Dec 29 2004

EXTENSIONS

More terms from Emeric Deutsch, Feb 16 2005

STATUS

approved

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Last modified July 26 16:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)