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A322815 Lexicographically earliest such sequence a that a(i) = a(j) => A048675(i) = A048675(j) for all i, j.

%I A322815 #13 Dec 10 2023 17:56:23
%S A322815 1,2,3,3,4,5,6,5,4,7,8,4,9,10,11,4,12,7,13,11,14,15,16,7,6,17,11,14,
%T A322815 18,19,20,7,21,22,23,11,24,25,26,19,27,28,29,21,6,30,31,11,8,10,32,26,
%U A322815 33,19,34,28,35,36,37,6,38,39,23,11,40,41,42,32,43,44,45,19,46,47,14,35,48,49,50,6,6,51,52,23,53,54,55,41,56,10,57,43,58,59,60,19,61,15,34,14
%N A322815 Lexicographically earliest such sequence a that a(i) = a(j) => A048675(i) = A048675(j) for all i, j.
%C A322815 Restricted growth sequence transform of A048675.
%C A322815 For all i, j > 1:
%C A322815   a(i) = a(j) => A277892(i) = A277892(j),
%C A322815   a(i) = a(j) => A322812(i) = A322812(j).
%H A322815 Antti Karttunen, <a href="/A322815/b322815.txt">Table of n, a(n) for n = 1..65537</a>
%o A322815 (PARI) up_to = 65537;
%o A322815 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 A322815 A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
%o A322815 v322815 = rgs_transform(vector(up_to,n,A048675(n)));
%o A322815 A322815(n) = v322815[n];
%Y A322815 Cf. A046523, A048675, A277892, A322812, A322816.
%K A322815 nonn
%O A322815 1,2
%A A322815 _Antti Karttunen_, Dec 27 2018