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%I #13 Dec 20 2018 02:11:47
%S 1,1,2,2,3,2,4,3,5,3,6,7,8,4,9,9,10,5,11,12,8,6,13,12,14,8,15,16,17,9,
%T 18,10,19,10,20,16,21,11,20,22,23,8,24,25,26,13,27,28,29,14,30,31,32,
%U 15,23,33,21,17,34,28,35,18,36,30,37,19,38,39,40,20,41,31,42,21,43,44,35,20,45,46,47,23,48,31,49,24,50,51,52,26,42,53,35,27,42,39,54,29
%N Lexicographically earliest such sequence a that a(i) = a(j) => A322351(i) = A322351(j) and A322352(i) = A322352(j), for all i, j.
%C Restricted growth sequence transform of the ordered pair [A322351(n), A322352(n)].
%C Essentially also the restricted growth sequence transform of the unordered pair {A003557(n), A173557(n)}.
%C For all i, j:
%C A295887(i) = A295887(j) => a(i) = a(j),
%C a(i) = a(j) => A322320(i) = A322320(j),
%C a(i) = a(j) => A322321(i) = A322321(j),
%C a(i) = a(j) => A000010(i) = A000010(j).
%H Antti Karttunen, <a href="/A322355/b322355.txt">Table of n, a(n) for n = 1..65537</a>
%o (PARI)
%o up_to = 65537;
%o 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 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
%o A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
%o A322351(n) = min(A003557(n), A173557(n));
%o A322352(n) = max(A003557(n), A173557(n));
%o v322355 = rgs_transform(vector(up_to, n, [A322351(n), A322352(n)]));
%o A322355(n) = v322355[n];
%Y Cf. A000010, A003557, A173557, A295887, A322320, A322321, A322351, A322352.
%K nonn
%O 1,3
%A _Antti Karttunen_, Dec 05 2018
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