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%I #45 Dec 06 2020 09:31:01
%S 1,0,-1,0,0,-1,0,1,1,0,0,0,0,0,-1,0,0,1,1,1,0,0,0,0,0,0,0,-1,0,-1,-1,
%T 0,0,0,0,-1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,
%U -1,0,0,-1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0
%N Regular triangle where T(n,k) = Sum (-1)^i, where the sum is over all factorizations of n into i factors that are all > 1 and <= k.
%F T(1,k) = 1, T(n,k) = -Sum_{d|n, 1 < d <= k} T(n/d,d).
%e Triangle begins:
%e 1
%e 0 -1
%e 0 0 -1
%e 0 1 1 0
%e 0 0 0 0 -1
%e 0 0 1 1 1 0
%e 0 0 0 0 0 0 -1
%e 0 -1 -1 0 0 0 0 -1
%e 0 0 1 1 1 1 1 1 0
%e 0 0 0 0 1 1 1 1 1 0
%e 0 0 0 0 0 0 0 0 0 0 -1
%e 0 0 -1 0 0 1 1 1 1 1 1 0
%e 0 0 0 0 0 0 0 0 0 0 0 0 -1
%e 0 0 0 0 0 0 1 1 1 1 1 1 1 0
%e 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0
%e 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1
%e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
%e 0 0 -1 -1 -1 0 0 0 1 1 1 1 1 1 1 1 1 0
%e 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
%e 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0
%t u[n_,k_]:=If[n==1,1,-Sum[u[n/d,d],{d,Select[Rest[Divisors[n]],#<=k&]}]]
%t Table[u[n,k],{n,20},{k,n}]
%Y Cf. A001055, A045778, A066032, A114592, A162247, A316441, A319237, A319238, A320835, A320836.
%Y Cf. A195017, A281118, A317145, A317176, A330935.
%K sign,tabl
%O 1
%A _Gus Wiseman_, Oct 22 2018
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