A341068 - OEIS

%I #6 Feb 04 2021 17:29:19

%S 1,8,36,112,274,568,1072,1912,3263,5280,8128,12048,17474,24824,34428,

%T 46600,62163,82160,107452,138392,176116,222560,279756,348168,428954,

%U 524848,639976,775448,932376,1113808,1326748,1573656,1855767,2175728,2544048,2965280,3441568,3974744,4580060

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

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

%p b:= proc(n, t) option remember;

%p       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(

%p       `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))

%p     end:

%p a:= n-> b(n, 8):

%p seq(a(n), n=8..46);  # _Alois P. Heinz_, Feb 04 2021

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

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

%K nonn

%O 8,2

%A _Ilya Gutkovskiy_, Feb 04 2021