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A100346 Number of compositions of n into divisors of n. 13
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); (Deutsch)

# 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 * A319352 A300834 A293214

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 January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)