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A322315 Lexicographically earliest such sequence a that a(i) = a(j) => A185633(i) = A185633(j) for all i, j.

%I A322315 #6 Dec 03 2018 18:30:39
%S A322315 1,2,1,3,1,4,1,5,1,6,1,7,1,2,1,8,1,9,1,10,1,11,1,12,1,2,1,13,1,14,1,
%T A322315 15,1,2,1,16,1,2,1,17,1,18,1,19,1,20,1,21,1,6,1,22,1,23,1,24,1,25,1,
%U A322315 26,1,2,1,27,1,28,1,3,1,29,1,30,1,2,1,3,1,31,1,32,1,33,1,34,1,2,1,35,1,36,1,37,1,2,1,38,1,2,1,39,1,40,1,41,1
%N A322315 Lexicographically earliest such sequence a that a(i) = a(j) => A185633(i) = A185633(j) for all i, j.
%C A322315 Restricted growth sequence transform of A185633.
%C A322315 For all i, j: a(i) = a(j) => A322313(i) = A322313(j).
%H A322315 Antti Karttunen, <a href="/A322315/b322315.txt">Table of n, a(n) for n = 1..65537</a>
%o A322315 (PARI)
%o A322315 up_to = 65537;
%o A322315 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 A322315 A185633(n) = { my(m=1); fordiv(n, d, if(isprime(1+d), m *= (1+d)^(1+valuation(n,1+d)))); (m); };
%o A322315 v322315 = rgs_transform(vector(up_to, n, A185633(n)));
%o A322315 A322315(n) = v322315[n];
%Y A322315 Cf. A185633, A322313.
%K A322315 nonn
%O A322315 1,2
%A A322315 _Antti Karttunen_, Dec 03 2018