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A336150 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A020639(i) = A020639(j), for all i, j >= 1.

%I A336150 #5 Jul 11 2020 17:57:31
%S A336150 1,2,3,2,4,5,6,2,3,5,7,5,8,5,9,2,10,5,11,5,9,5,12,5,4,5,3,5,13,14,15,
%T A336150 2,9,5,16,5,17,5,9,5,18,14,19,5,9,5,20,5,6,5,9,5,21,5,16,5,9,5,22,14,
%U A336150 23,5,9,2,16,14,24,5,9,14,25,5,26,5,9,5,27,14,28,5,3,5,29,14,16,5,9,5,30,14,27,5,9,5,16,5,31,5,9,5,32,14,33,5,34
%N A336150 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A020639(i) = A020639(j), for all i, j >= 1.
%C A336150 Restricted growth sequence transform of the ordered pair [A001221(n), A020639(n)]. The first member of pair gives the number of distinct prime divisors of n, and the second member gives its smallest prime factor.
%C A336150 For all i, j: A324400(i) = A324400(j) => a(i) = a(j).
%H A336150 Antti Karttunen, <a href="/A336150/b336150.txt">Table of n, a(n) for n = 1..65537</a>
%o A336150 (PARI)
%o A336150 up_to = 65537;
%o A336150 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 A336150 A020639(n) = if(1==n, n, factor(n)[1, 1]);
%o A336150 Aux336150(n) = [omega(n), A020639(n)];
%o A336150 v336150 = rgs_transform(vector(up_to, n, Aux336150(n)));
%o A336150 A336150(n) = v336150[n];
%Y A336150 Cf. A001221, A020639.
%Y A336150 Cf. also A324400, A336151, A336152.
%K A336150 nonn
%O A336150 1,2
%A A336150 _Antti Karttunen_, Jul 11 2020