A293521 - OEIS

%I #13 Oct 18 2017 08:56:11

%S 0,1,1,3,3,2,5,9,8,11,15,24,30,42,51,76,94,126,158,217,298,403,539,

%T 731,970,1305,1748,2322,3179,4225,5715,7596,10259,13731,18357,24771,

%U 33184,44448,59968,80764,107973,145638,195237,262446,352904,474964,637081,856232,1149966,1543986,2076534,2789516

%N Number of surviving (but not bifurcating) nodes at generation n in the binary tree of persistently squarefree numbers (see A293230).

%F a(n) = Sum_{k=(2^n)..(2^(1+n))-1)] abs(A293233(k)) * [1==(A008966(2k)+A008966(1+2k))].

%F a(n) = A293518(n) + A293519(n). [even survivors + odd survivors.]

%e a(2) = 1 because in the binary tree illustrated in A293230, there is only one node at the level (namely, the node 6) that spawns just one offspring.

%o (PARI) \\ See program at A293520.

%Y Cf. A293230, A293441, A293518, A293519, A293520, A293522.

%K nonn

%O 0,4

%A _Antti Karttunen_, Oct 12 2017