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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 26 2016
STATUS
approved