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%I #11 Jul 15 2015 06:40:08
%S 0,1,1,1,1,1,3,1,3,2,3,1,7,1,3,3,6,1,8,1,7,3,3,1,17,2,3,4,7,1,13,1,12,
%T 3,3,3,24,1,3,3,17,1,13,1,7,8,3,1,40,2,8,3,7,1,20,3,17,3,3,1,41,1,3,8,
%U 24,3,13,1,7,3,13,1,68,1,3,8,7,3,13,1,40,8,3,1,41,3,3,3,17,1,44,3,7,3,3,3
%N Number of double-perfect partitions of [1..n].
%H Alois P. Heinz, <a href="/A117621/b117621.txt">Table of n, a(n) for n = 1..20000</a>
%H HoKyu Lee, <a href="http://dx.doi.org/10.1016/j.disc.2006.01.007">Double perfect partitions</a>, Discrete Math., 306 (2006), 519-525.
%F a(1)=0; a(n)=1 for n=2..5; a(n) = Sum_{m=2..n-1, m-1|n-1} a(m) for n >= 6.
%p f:=proc(n) option remember; local t1,m,nm1,mm1; nm1:=n-1; if n <= 1 then RETURN(0); elif n <= 5 then RETURN(1); else t1:=0; for m from 2 to n-1 do mm1:=m-1; if nm1 mod mm1 = 0 then t1:=t1+f(m); fi; od; RETURN(t1); fi; end;
%p # second Maple program:
%p with(numtheory):
%p a:= proc(n) option remember; `if`(n<6, [0, 1$4][n],
%p add(a(k+1), k=divisors(n-1) minus {n-1}))
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jul 09 2015
%t a[n_] := a[n] = If[n<6, {0, 1, 1, 1, 1}[[n]], Sum[a[k+1], {k, Divisors[n-1] ~Complement~ {n-1}}]]; Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jul 15 2015, after _Alois P. Heinz_ *)
%Y Cf. A002033.
%K nonn
%O 1,7
%A _N. J. A. Sloane_, Apr 07 2006
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