A341068 Number of ways to write n as an ordered sum of 8 squarefree numbers.

1, 8, 36, 112, 274, 568, 1072, 1912, 3263, 5280, 8128, 12048, 17474, 24824, 34428, 46600, 62163, 82160, 107452, 138392, 176116, 222560, 279756, 348168, 428954, 524848, 639976, 775448, 932376, 1113808, 1326748, 1573656, 1855767, 2175728, 2544048, 2965280, 3441568, 3974744, 4580060

Offset

8,2

Links

Table of n, a(n) for n=8..46.

Formula

G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^8.

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..46);  # Alois P. Heinz, Feb 04 2021

Mathematica

nmax = 46; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

Crossrefs

Cf. A005117, A008683, A008966, A098235, A280210, A326443, A341064, A341065, A341066, A341067, A341069, A341070.

Sequence in context: A325656 A357716 A341987 * A092365 A014343 A162596

Adjacent sequences: A341065 A341066 A341067 * A341069 A341070 A341071

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved