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A378602 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A119347(i) = A119347(j), for all i, j >= 1.

%I A378602 #6 Dec 01 2024 19:54:40
%S A378602 1,2,2,3,2,4,2,5,3,6,2,7,2,6,6,8,2,9,2,10,6,6,2,11,3,6,5,12,2,13,2,14,
%T A378602 6,6,6,15,2,6,6,16,2,17,2,18,19,6,2,20,3,18,6,18,2,21,6,21,6,6,2,22,2,
%U A378602 6,23,24,6,25,2,18,6,26,2,27,2,6,18,18,6,28,2,29,8,6,2,30,6,6,6,31,2,32,6,18,6,6,6,33,2,18,23,34,2,28,2,35,36
%N A378602 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A119347(i) = A119347(j), for all i, j >= 1.
%C A378602 Restricted growth sequence transform of the ordered pair [A046523(n), A119347(n)].
%H A378602 Antti Karttunen, <a href="/A378602/b378602.txt">Table of n, a(n) for n = 1..100000</a>
%o A378602 (PARI)
%o A378602 up_to = 100000;
%o A378602 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 A378602 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A378602 A119347(n) = { my(c=[0]); fordiv(n,d, c = Set(concat(c,vector(#c,i,c[i]+d)))); (#c)-1; };
%o A378602 Aux378602(n) = [A046523(n), A119347(n)];
%o A378602 v378602 = rgs_transform(vector(up_to, n, Aux378602(n)));
%o A378602 A378602(n) = v378602[n];
%Y A378602 Cf. A046523, A119347, A101296.
%Y A378602 Cf. also A378601, A378603.
%K A378602 nonn
%O A378602 1,2
%A A378602 _Antti Karttunen_, Dec 01 2024