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A378601 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A083206(i) = A083206(j), for all i, j >= 1.

%I A378601 #6 Dec 01 2024 19:54:35
%S A378601 1,2,2,3,2,4,2,5,3,6,2,7,2,6,6,8,2,9,2,7,6,6,2,10,3,6,5,7,2,11,2,12,6,
%T A378601 6,6,13,2,6,6,14,2,15,2,9,9,6,2,16,3,9,6,9,2,14,6,17,6,6,2,18,2,6,9,
%U A378601 19,6,15,2,9,6,20,2,21,2,6,9,9,6,15,2,22,8,6,2,23,6,6,6,17,2,24,6,9,6,6,6,25,2,9,9,13,2,15,2,17,26
%N A378601 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A083206(i) = A083206(j), for all i, j >= 1.
%C A378601 Restricted growth sequence transform of the ordered pair [A046523(n), A083206(n)].
%H A378601 Antti Karttunen, <a href="/A378601/b378601.txt">Table of n, a(n) for n = 1..100000</a>
%o A378601 (PARI)
%o A378601 up_to = 100000;
%o A378601 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 A378601 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A378601 v083206 = readvec("b083206_to.txt"); \\ Precomputed with A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };
%o A378601 A083206(n) = v083206[n];
%o A378601 Aux378601(n) = [A046523(n), A083206(n)];
%o A378601 v378601 = rgs_transform(vector(up_to, n, Aux378601(n)));
%o A378601 A378601(n) = v378601[n];
%Y A378601 Cf. A046523, A083206, A101296.
%Y A378601 Cf. also A378602, A378602, A378603, A378604.
%K A378601 nonn
%O A378601 1,2
%A A378601 _Antti Karttunen_, Dec 01 2024