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

0,5

Comments

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

Links

Table of n, a(n) for n=0..72.

Eric Weisstein's World of Mathematics, Squarefree

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A005117, A008683, A098235.

Cf. A098238, A121550.

Sequence in context: A359263 A296693 A282585 * A023982 A189092 A287268

Adjacent sequences: A280207 A280208 A280209 * A280211 A280212 A280213

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2016

Status

approved