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A322868 Lexicographically earliest such sequence a that a(i) = a(j) => A278222(A048675(i)) = A278222(A048675(j)) for all i, j.

%I A322868 #10 Dec 31 2018 13:23:19
%S A322868 1,2,2,2,2,3,2,3,2,4,2,2,2,4,3,2,2,4,2,3,4,4,2,4,2,4,3,4,2,5,2,4,4,4,
%T A322868 3,3,2,4,4,5,2,6,2,4,2,4,2,3,2,4,4,4,2,5,4,6,4,4,2,2,2,4,3,3,4,6,2,4,
%U A322868 4,6,2,5,2,4,4,4,3,6,2,2,2,4,2,3,4,4,4,6,2,4,4,4,4,4,4,5,2,4,4,4,2,6,2,6,5
%N A322868 Lexicographically earliest such sequence a that a(i) = a(j) => A278222(A048675(i)) = A278222(A048675(j)) for all i, j.
%C A322868 Restricted growth sequence transform of A278222(A048675(n)), or equivalently, of A278222(A322821(n)).
%C A322868 For all i, j: a(i) = a(j) => A322869(i) = A322869(j).
%H A322868 Antti Karttunen, <a href="/A322868/b322868.txt">Table of n, a(n) for n = 1..65537</a>
%H A322868 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A322868 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A322868 (PARI)
%o A322868 up_to = 8192;
%o A322868 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 A322868 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A322868 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A322868 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; \\ From A048675
%o A322868 A278222(n) = A046523(A005940(1+n));
%o A322868 v322868 = rgs_transform(vector(up_to,n,A278222(A048675(n))));
%o A322868 A322868(n) = v322868[n];
%Y A322868 Cf. A005940, A046523, A048675, A278222, A322821, A322861, A322869.
%K A322868 nonn
%O A322868 1,2
%A A322868 _Antti Karttunen_, Dec 31 2018