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A322314 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(i) = A046523(j) and A322312(i) = A322312(j), for all i, j.

%I A322314 #5 Dec 03 2018 18:30:30
%S A322314 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,13,11,8,3,14,7,10,15,16,3,
%T A322314 17,3,18,11,10,11,19,3,10,11,14,3,20,3,16,21,8,3,22,7,23,11,16,3,24,
%U A322314 11,25,11,8,3,26,3,10,21,27,11,17,3,28,11,29,3,30,3,10,21,28,11,31,3,22,32,8,3,33,11,10,11,34,3,35,11,16,11,10,11,36,3,37,21,38
%N A322314 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(i) = A046523(j) and A322312(i) = A322312(j), for all i, j.
%C A322314 Restricted growth sequence transform of the ordered pair [A046523(n), A322312(n)].
%H A322314 Antti Karttunen, <a href="/A322314/b322314.txt">Table of n, a(n) for n = 1..65537</a>
%o A322314 (PARI)
%o A322314 up_to = 65537;
%o A322314 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 A322314 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A322314 A322312(n) = { my(m=1,p); fordiv(n,d,p=1+d; if(isprime(p), for(i=0,oo,if(n%(p^i),m *= prime(i);break)))); (m); };
%o A322314 v322314 = rgs_transform(vector(up_to, n, [A046523(n), A322312(n)]));
%o A322314 A322314(n) = v322314[n];
%Y A322314 Cf. A046523, A322312, A322313.
%K A322314 nonn
%O A322314 1,2
%A A322314 _Antti Karttunen_, Dec 03 2018