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%I A322588 #5 Dec 18 2018 17:04:35
%S A322588 1,2,3,4,3,5,3,6,7,8,3,9,3,10,10,11,3,12,3,13,14,15,3,16,17,18,19,20,
%T A322588 3,21,3,22,23,24,23,25,3,26,27,28,3,29,3,30,31,21,3,32,33,34,21,35,3,
%U A322588 36,21,37,38,39,3,40,3,29,41,42,43,44,3,45,29,44,3,46,3,47,48,49,29,50,3,51,52,53,3,54,55,56,57,58,3,59,60,40,61,44,57,62,3,63,64,65,3,66,3
%N A322588 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and f(n) = A291750(n) for any other number.
%C A322588 For all i, j: a(i) = a(j) => A322318(i) = A322318(j).
%H A322588 Antti Karttunen, <a href="/A322588/b322588.txt">Table of n, a(n) for n = 1..65537</a>
%o A322588 (PARI)
%o A322588 up_to = 65537;
%o A322588 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 A322588 A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A322588 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A322588 Aux322588(n) = if((n>2)&&isprime(n),0,(1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n)));
%o A322588 v322588 = rgs_transform(vector(up_to, n, Aux322588(n)));
%o A322588 A322588(n) = v322588[n];
%Y A322588 Cf. A291750, A291751, A322587, A322589, A322591, A322592.
%K A322588 nonn
%O A322588 1,2
%A A322588 _Antti Karttunen_, Dec 18 2018

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