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A322022 Lexicographically earliest such sequence a that a(i) = a(j) => A305891(i) = A305891(j) and A319697(i) = A319697(j), for all i, j.

%I A322022 #7 Jan 19 2019 04:15:43
%S A322022 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,11,15,3,16,7,17,18,19,3,
%T A322022 20,3,21,11,22,11,23,3,24,11,25,3,26,3,27,28,29,3,30,7,31,11,32,3,33,
%U A322022 11,34,11,35,3,36,3,37,28,38,11,39,3,40,11,39,3,41,3,42,28,43,11,44,3,45,46,47,3,48,11,49,11,50,3,51,11,52,11,53,11,54,3,55,28
%N A322022 Lexicographically earliest such sequence a that a(i) = a(j) => A305891(i) = A305891(j) and A319697(i) = A319697(j), for all i, j.
%C A322022 Restricted growth sequence transform of the ordered pair [A305891(n), A319697(n)], or equally, of the triple [A007814(n), A046523(n), A319697(n)].
%H A322022 Antti Karttunen, <a href="/A322022/b322022.txt">Table of n, a(n) for n = 1..65537</a>
%o A322022 (PARI)
%o A322022 up_to = 65537;
%o A322022 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 A322022 A007814(n) = valuation(n,2);
%o A322022 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A322022 A319697(n) = sumdiv(n, d, (!(d%2))*issquarefree(d)*d);
%o A322022 v322022 = rgs_transform(vector(up_to, n, [A007814(n), A046523(n), A319697(n)]));
%o A322022 A322022(n) = v322022[n];
%Y A322022 Cf. A007814, A046523, A097272, A305891, A319697, A319698, A322021.
%K A322022 nonn
%O A322022 1,2
%A A322022 _Antti Karttunen_, Nov 29 2018