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A325561 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A234741(n) except for those numbers for which A234741(n) = n, in which case f(n) = 0.

%I A325561 #6 May 11 2019 02:23:23
%S A325561 1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,3,1,1,4,1,1,1,5,1,6,1,1,1,1,1,7,1,
%T A325561 8,9,1,1,10,1,1,11,1,1,5,1,1,1,12,13,1,1,1,14,15,1,16,1,1,1,1,1,8,1,
%U A325561 17,18,1,1,17,19,1,20,1,1,21,1,22,23,1,1,5,1,1,24,1,1,15,1,1,13,25,1,26,1,1,1,1,27,15,28,1,1,1,1,29
%N A325561 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A234741(n) except for those numbers for which A234741(n) = n, in which case f(n) = 0.
%C A325561 For all i, j:
%C A325561   A305801(i) = A305801(j) => a(i) = a(j) => A325562(i) = A325562(j).
%H A325561 Antti Karttunen, <a href="/A325561/b325561.txt">Table of n, a(n) for n = 1..65537</a>
%H A325561 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%o A325561 (PARI)
%o A325561 up_to = 65537;
%o A325561 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A325561 A234741(n) = {n=factor(n); n[, 1]=apply(t->Pol(binary(t)), n[, 1]); sum(i=1, #n=Vec(factorback(n))%2, n[i]<<(#n-i))}; \\ From A234741
%o A325561 Aux325561(n) = { my(u=A234741(n)); if(u==n,0,u); };
%o A325561 v325561 = rgs_transform(vector(up_to,n,Aux325561(n)));
%o A325561 A325561(n) = v325561[n];
%Y A325561 Cf. A234741, A305801, A325562.
%K A325561 nonn
%O A325561 1,9
%A A325561 _Antti Karttunen_, May 10 2019