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a(n) = A297112(A005940(1+n)), where A297112 is the Möbius transform of A156552 [the inverse of map n -> A005940(1+n)].
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%I #18 Aug 07 2023 08:32:21

%S 0,1,2,2,4,2,4,4,8,4,4,4,8,4,8,8,16,8,8,8,8,4,8,8,16,8,8,8,16,8,16,16,

%T 32,16,16,16,16,8,16,16,16,8,8,8,16,8,16,16,32,16,16,16,16,8,16,16,32,

%U 16,16,16,32,16,32,32,64,32,32,32,32,16,32,32,32,16,16,16,32,16,32,32,32,16,16,16,16,8,16,16

%N a(n) = A297112(A005940(1+n)), where A297112 is the Möbius transform of A156552 [the inverse of map n -> A005940(1+n)].

%H Antti Karttunen, <a href="/A364567/b364567.txt">Table of n, a(n) for n = 0..16383</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F For n > 0, a(n) = 2^A033265(n).

%o (PARI) A364567(n) = if(!n,n, my(i=1); while(n>1, if((n%4)!=1, i<<=1); n >>= 1); (i));

%Y Cf. A005940, A033265, A156552, A297112, A364568.

%Y Cf. also A364571.

%K nonn

%O 0,3

%A _Antti Karttunen_, Aug 05 2023