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A280544
Expansion of 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k), where d(k) is the number of divisors (A000005).
1
1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 3, 0, 5, 2, 8, 3, 13, 5, 22, 10, 34, 18, 58, 31, 94, 57, 153, 99, 254, 172, 417, 302, 685, 523, 1136, 901, 1872, 1557, 3097, 2673, 5133, 4577, 8505, 7843, 14109, 13380, 23440, 22816, 38953, 38855, 64789, 66053, 107871, 112190, 179664, 190369, 299478, 322683, 499501, 546548
OFFSET
0,9
COMMENTS
Number of compositions (ordered partitions) of n into composite parts (A002808).
FORMULA
G.f.: 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k).
EXAMPLE
a(10) = 3 because we have [10], [6, 4] and [4, 6].
MATHEMATICA
nmax = 59; CoefficientList[Series[1/(1 - Sum[(1 - Floor[2/DivisorSigma[0, k]]) x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
PROG
(PARI) x='x+O('x^60); Vec(1/(1 - sum(k=2, 59, (1 - 2\numdiv(k))*x^k))) \\ Indranil Ghosh, Apr 03 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 05 2017
STATUS
approved