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%I #6 Jan 08 2019 19:08:34
%S 1,2,3,4,3,5,3,6,3,7,3,8,3,9,3,10,3,11,3,12,3,13,3,14,3,15,3,16,3,17,
%T 3,18,3,19,3,20,3,21,3,22,3,23,3,24,3,17,3,25,3,26,3,27,3,28,3,29,3,
%U 30,3,31,3,23,3,32,3,33,3,34,3,33,3,35,3,36,3,37,3,38,3,39,3,40,3,41,3,42,3,43,3,44,3,31,3,33,3,45,3,46,3,47,3,48,3,49,3
%N Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A291750(n) for all n, except for odd numbers n > 1, f(n) = 0.
%C For all i, j:
%C A319701(i) = A319701(j) => a(i) = a(j),
%C a(i) = a(j) => A146076(i) = A146076(j),
%C a(i) = a(j) => A319697(i) = A319697(j).
%H Antti Karttunen, <a href="/A323238/b323238.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o Aux323238(n) = if((n>1)&&(n%2),0,(1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n)));
%o v323238 = rgs_transform(vector(up_to, n, Aux323238(n)));
%o A323238(n) = v323238[n];
%Y Cf. A003557, A048250, A146076, A291750, A291751, A319698, A319697, A319701, A322588, A323237, A323241.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 08 2019
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