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A280128 Expansion of Product_{k>=2} (1 + mu(k)^2*x^k), where mu(k) is the Moebius function (A008683). 3
1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 3, 3, 5, 4, 6, 7, 7, 9, 9, 11, 13, 14, 16, 19, 18, 24, 23, 28, 31, 33, 39, 42, 46, 52, 57, 63, 71, 76, 87, 92, 103, 113, 123, 135, 149, 161, 178, 193, 210, 231, 249, 274, 298, 323, 352, 382, 414, 451, 486, 528, 572, 617, 669 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Number of partitions of n into distinct 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 + mu(k)^2*x^k).

EXAMPLE

G.f. = 1 + x^2 + x^3 + 2*x^5 + x^6 + 2*x^7 + 2*x^8 + 2*x^9 + 3*x^10 + 3*x^11 + ...

a(10) = 3 because we have [10], [7, 3] and [5, 3, 2].

MAPLE

with(numtheory): seq(coeff(series(mul(1+mobius(k)^2*x^k, k=2..n), x, n+1), x, n), n=0..70); # Muniru A Asiru, Jul 30 2018

MATHEMATICA

nmax = 75; CoefficientList[Series[Product[1 + MoebiusMu[k]^2 x^k, {k, 2, nmax}], {x, 0, nmax}], x]

PROG

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

CROSSREFS

Cf. A005117, A008683, A087188, A144338, A280127.

Sequence in context: A054705 A025800 A029258 * A070096 A319821 A024154

Adjacent sequences:  A280125 A280126 A280127 * A280129 A280130 A280131

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 26 2016

STATUS

approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)