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A320225 a(1) = 1; a(n > 1) = Sum_{k = 1..n} Sum_{d|k, d < k} a(d).

%I A320225 #22 Jan 22 2023 20:44:54
%S A320225 1,1,2,4,5,9,10,16,19,26,27,44,45,57,65,87,88,120,121,158,171,200,201,
%T A320225 278,284,331,353,426,427,536,537,646,676,766,782,982,983,1106,1154,
%U A320225 1365,1366,1617,1618,1851,1943,2146,2147,2589,2600,2917,3008,3390,3391
%N A320225 a(1) = 1; a(n > 1) = Sum_{k = 1..n} Sum_{d|k, d < k} a(d).
%H A320225 Seiichi Manyama, <a href="/A320225/b320225.txt">Table of n, a(n) for n = 1..10000</a>
%F A320225 a(1) = 1; a(n > 1) = Sum_{d = 1..n-1} a(d) * floor(n/d-1).
%F A320225 G.f. A(x) satisfies A(x) = x + (1/(1 - x)) * Sum_{k>=2} A(x^k). - _Ilya Gutkovskiy_, Sep 06 2019
%t A320225 sau[n_]:=If[n==1,1,Sum[sau[d],{k,n},{d,Most[Divisors[k]]}]];
%t A320225 Table[sau[n],{n,30}]
%o A320225 (Python)
%o A320225 from functools import lru_cache
%o A320225 @lru_cache(maxsize=None)
%o A320225 def A320225(n): return 1 if n == 1 else sum(A320225(d)*(n//d-1) for d in range(1,n)) # _Chai Wah Wu_, Jun 08 2022
%Y A320225 Cf. A002541, A003238, A010766, A014668, A126656, A167865, A316782, A317712, A320222, A320224.
%K A320225 nonn
%O A320225 1,3
%A A320225 _Gus Wiseman_, Oct 07 2018