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A323369 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) = A323368(n) for any other number.

%I A323369 #8 Jan 12 2019 20:47:06
%S A323369 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,19,20,21,
%T A323369 3,22,3,23,24,25,24,26,3,27,28,29,3,30,3,31,32,22,3,33,34,35,36,37,3,
%U A323369 38,36,39,40,41,3,42,3,30,43,44,45,46,3,47,48,46,3,49,3,50,51,52,48,53,3,54,55,56,3,57,58,59,60,61,3,62,63,42,64,46,60,65,3,66,67,68,3,69,3
%N A323369 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) = A323368(n) for any other number.
%C A323369 Restricted growth sequence transform of function f, where f(n) = 0 for odd primes, and for any other number, f(n) = [A000035(n), A003557(n), A048250(n)].
%C A323369 For all i, j:
%C A323369   A305801(i) = A305801(j) => a(i) = a(j),
%C A323369   a(i) = a(j) => A007814(i) = A007814(j),
%C A323369   a(i) = a(j) => A322588(i) = A322588(j),
%C A323369   a(i) = a(j) => A323238(i) = A323238(j).
%H A323369 Antti Karttunen, <a href="/A323369/b323369.txt">Table of n, a(n) for n = 1..65537</a>
%o A323369 (PARI)
%o A323369 up_to = 65537;
%o A323369 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 A323369 A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
%o A323369 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A323369 Aux323369(n) = if((n>2)&&isprime(n),0,[(n%2), A003557(n), A048250(n)]);
%o A323369 v323369 = rgs_transform(vector(up_to, n, Aux323369(n)));
%o A323369 A323369(n) = v323369[n];
%Y A323369 Cf. A000035, A003557, A048250, A291750, A291751, A305801, A322588, A323238, A323368.
%Y A323369 Cf. also A323367.
%K A323369 nonn
%O A323369 1,2
%A A323369 _Antti Karttunen_, Jan 12 2019