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A322990 a(n) = A289272(floor(A289271(n)/2)).

%I A322990 #10 Jan 02 2019 11:55:03
%S A322990 1,1,2,3,4,2,5,7,8,3,9,6,11,4,10,13,16,5,17,12,14,7,19,18,23,8,25,15,
%T A322990 27,6,29,31,22,9,20,21,32,11,26,28,37,10,41,24,36,13,43,34,47,16,38,
%U A322990 33,49,17,44,35,46,19,53,30,59,23,40,61,52,14,64,39,50,12,67,56,71,25,54,48,45,18,73,68,79,27,81,42,76,29,58,63,83,15,55,51,62,31,92
%N A322990 a(n) = A289272(floor(A289271(n)/2)).
%C A322990 For all n > 1, in the binary tree illustrated in A289272, the node which contains (has value) n, its parent node has value a(n).
%C A322990 Each n occurs exactly twice in this sequence.
%H A322990 Antti Karttunen, <a href="/A322990/b322990.txt">Table of n, a(n) for n = 1..16384</a>
%F A322990 a(n) = A289272(floor(A289271(n)/2)).
%o A322990 (PARI)
%o A322990 A289271(n) = { my(v=0,i=0,x=1); for(d=2,oo,if(n==1, return(v)); if(1==gcd(x,d)&&1==omega(d), if(!(n%d)&&1==gcd(d,n/d), v += 2^i; n /= d; x *= d); i++)); }; \\ After _Rémy Sigrist_'s program for A289271.
%o A322990 A289272(n) = { my(m=1, pp=1); while(n>0, pp++; while(!isprimepower(pp)||(gcd(pp,m)>1), pp++); if(n%2, m *= pp); n >>=1); (m); };
%o A322990 A322990(n) = A289272(A289271(n)>>1);
%Y A322990 Cf. A289271, A289272, A322988, A322991, A322992.
%Y A322990 Cf. also A252463, A300840.
%K A322990 nonn
%O A322990 1,3
%A A322990 _Antti Karttunen_, Jan 01 2019