%I #18 Jan 09 2019 19:26:06
%S 0,1,1,3,1,5,1,7,3,9,1,11,1,17,5,15,1,13,1,19,9,33,1,23,3,65,7,35,1,
%T 21,1,31,17,129,5,27,1,257,33,39,1,37,1,67,11,513,1,47,3,25,65,131,1,
%U 29,9,71,129,1025,1,43,1,2049,19,63,17,69,1,259,257,41,1,55,1,4097,13,515,5,133,1,79,15,8193,1,75,33,16385,513,135,1,45,9
%N a(1) = 0; for n > 1, a(n) = A000265(A156552(n)).
%H Antti Karttunen, <a href="/A322993/b322993.txt">Table of n, a(n) for n = 1..8192</a>
%F a(1) = 0; for n > 1, a(n) = A000265(A156552(n)).
%F For n > 1, a(n) = A156552(2*A246277(n)).
%F A000120(a(n)) = A001222(n) for all n >= 1.
%t Array[#/2^IntegerExponent[#, 2] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ #]] &, 91] (* _Michael De Vlieger_, Jan 03 2019 *)
%o (PARI)
%o A000265(n) = (n/2^valuation(n, 2));
%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
%o A322993(n) = if(1==n,0,A000265(A156552(n)));
%Y Cf. A000265, A156552, A246277, A305897 (restricted growth sequence transform), A322994 (Möbius transform).
%Y Cf. also A322995.
%K nonn,base
%O 1,4
%A _Antti Karttunen_, Jan 02 2019