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A341065 Number of ways to write n as an ordered sum of 5 squarefree numbers.

%I A341065 #6 Feb 04 2021 17:23:33
%S A341065 1,5,15,30,50,76,120,180,250,315,401,520,670,805,955,1160,1445,1715,
%T A341065 1980,2290,2741,3180,3605,4040,4690,5341,5985,6600,7490,8380,9251,
%U A341065 10060,11240,12415,13595,14670,16295,17850,19425,20780,22905,24905,26895,28600,31335,33966,36485,38620
%N A341065 Number of ways to write n as an ordered sum of 5 squarefree numbers.
%F A341065 G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^5.
%p A341065 b:= proc(n, t) option remember;
%p A341065       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341065       `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
%p A341065     end:
%p A341065 a:= n-> b(n, 5):
%p A341065 seq(a(n), n=5..52);  # _Alois P. Heinz_, Feb 04 2021
%t A341065 nmax = 52; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341065 Cf. A005117, A008683, A008966, A098235, A280210, A308840, A341064, A341066, A341067, A341068, A341069, A341070.
%K A341065 nonn
%O A341065 5,2
%A A341065 _Ilya Gutkovskiy_, Feb 04 2021