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A280127 Expansion of Product_{k>=2} 1/(1 - mu(k)^2*x^k), where mu(k) is the Moebius function (A008683). 4
1, 0, 1, 1, 1, 2, 3, 3, 4, 5, 7, 8, 11, 13, 16, 20, 24, 30, 35, 43, 52, 62, 74, 88, 104, 123, 146, 171, 201, 235, 275, 320, 373, 433, 502, 581, 672, 773, 891, 1024, 1176, 1348, 1543, 1764, 2013, 2296, 2614, 2974, 3378, 3833, 4345, 4920, 5565, 6288, 7098, 8005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Number of partitions of n into squarefree parts > 1 (A144338).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Joerg Arndt, Matters Computational (The Fxtbook), section 16.4.3 "Partitions into square-free parts", pp.351-352

Eric Weisstein's World of Mathematics, Squarefree

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=2} 1/(1 - mu(k)^2*x^k).

EXAMPLE

G.f. = 1 + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 4*x^8 + 5*x^9 + 7*x^10 + ...

a(9) = 5 because we have [7, 2], [6, 3], [5, 2, 2], [3, 3, 3] and [3, 2, 2, 2].

MAPLE

with(numtheory): seq(coeff(series(mul(1/(1-mobius(k)^2*x^k), k=2..n), x, n+1), x, n), n=0..60); # Muniru A Asiru, Jul 30 2018

MATHEMATICA

nmax = 65; CoefficientList[Series[Product[1/(1 - MoebiusMu[k]^2 x^k), {k, 2, nmax}], {x, 0, nmax}], x]

PROG

(PARI) {a(n) = if(n < 0, 0, polcoeff( 1 / prod(k=2, n, 1 - issquarefree(k)*x^k + x*O(x^n)), n))}; /* Michael Somos, Dec 26 2016 */

CROSSREFS

Cf. A005117, A008683, A073576, A144338, A280128.

Sequence in context: A125616 A141472 A029034 * A237977 A115339 A305631

Adjacent sequences:  A280124 A280125 A280126 * A280128 A280129 A280130

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 26 2016

STATUS

approved

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Last modified August 14 19:09 EDT 2020. Contains 336483 sequences. (Running on oeis4.)