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A341064 Number of ways to write n as an ordered sum of 4 squarefree numbers.

%I A341064 #6 Feb 04 2021 17:19:52
%S A341064 1,4,10,16,23,32,50,68,83,92,116,148,178,192,224,276,335,360,400,460,
%T A341064 547,580,634,704,821,868,938,1024,1162,1212,1288,1392,1572,1628,1742,
%U A341064 1876,2123,2172,2308,2460,2761,2820,2964,3176,3550,3628,3778,4028,4481,4528,4686,4932,5513,5564
%N A341064 Number of ways to write n as an ordered sum of 4 squarefree numbers.
%F A341064 G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^4.
%p A341064 b:= proc(n, t) option remember;
%p A341064       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341064       `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
%p A341064     end:
%p A341064 a:= n-> b(n, 4):
%p A341064 seq(a(n), n=4..57);  # _Alois P. Heinz_, Feb 04 2021
%t A341064 nmax = 57; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^4, {x, 0, nmax}], x] // Drop[#, 4] &
%Y A341064 Cf. A005117, A008683, A008966, A098235, A280210, A308767, A341065, A341066, A341067, A341068, A341069, A341070.
%K A341064 nonn
%O A341064 4,2
%A A341064 _Ilya Gutkovskiy_, Feb 04 2021