A280210 Expansion of (Sum_{k>=1} mu(k)^2*x^k)^3, where mu(k) is the Moebius function (A008683).

0, 0, 0, 1, 3, 6, 7, 9, 12, 19, 21, 21, 21, 30, 36, 37, 36, 48, 58, 63, 57, 70, 78, 87, 78, 96, 105, 114, 105, 123, 133, 138, 126, 148, 162, 174, 156, 195, 207, 220, 192, 234, 250, 261, 237, 280, 312, 318, 282, 330, 363, 370, 315, 375, 405, 432, 366, 421, 453, 483, 417, 468, 507, 532, 474, 537, 568, 591, 519, 601, 630, 666, 570

Offset: 0

Author

Ilya Gutkovskiy, Dec 29 2016

Keywords

• nonn

Comments

Number of ordered ways of writing n as sum of three squarefree numbers (A005117).

Examples

			a(4) = 3 because we have [2, 1, 1], [1, 2, 1] and [1, 1, 2].
		

Links

• Eric Weisstein's World of Mathematics, Squarefree

Crossrefs

Cf. A005117, A008683, A098235.

Cf. A098238, A121550.

Programs

Mathematica

nmax = 72; CoefficientList[Series[(Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}])^3, {x, 0, nmax}], x]

Formula

G.f.: (Sum_{k>=1} mu(k)^2*x^k)^3.