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A341067 Number of ways to write n as an ordered sum of 7 squarefree numbers.

%I A341067 #8 Feb 11 2021 12:11:40
%S A341067 1,7,28,77,168,315,553,932,1505,2282,3297,4634,6447,8771,11607,15029,
%T A341067 19390,24885,31500,39137,48335,59584,73003,88109,105525,126112,150472,
%U A341067 177632,208160,243194,284102,329357,379379,435477,500108,571124,648998,735112,833483,940765,1057679
%N A341067 Number of ways to write n as an ordered sum of 7 squarefree numbers.
%H A341067 Alois P. Heinz, <a href="/A341067/b341067.txt">Table of n, a(n) for n = 7..10000</a>
%F A341067 G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^7.
%p A341067 b:= proc(n, t) option remember;
%p A341067       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
%p A341067       `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
%p A341067     end:
%p A341067 a:= n-> b(n, 7):
%p A341067 seq(a(n), n=7..47);  # _Alois P. Heinz_, Feb 04 2021
%t A341067 nmax = 47; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y A341067 Cf. A005117, A008683, A008966, A098235, A280210, A308952, A341064, A341065, A341066, A341068, A341069, A341070.
%K A341067 nonn
%O A341067 7,2
%A A341067 _Ilya Gutkovskiy_, Feb 04 2021