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A378603 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A033630(i) = A033630(j), for all i, j >= 1.

%I A378603 #6 Dec 01 2024 19:54:45
%S A378603 1,2,2,3,2,4,2,5,3,6,2,7,2,6,6,8,2,7,2,9,6,6,2,10,3,6,5,9,2,11,2,12,6,
%T A378603 6,6,13,2,6,6,14,2,15,2,16,16,6,2,17,3,16,6,16,2,14,6,18,6,6,2,19,2,6,
%U A378603 16,20,6,15,2,16,6,21,2,22,2,6,16,16,6,23,2,24,8,6,2,25,6,6,6,26,2,27,6,16,6,6,6,28,2,16,16,29,2,23,2,26,21
%N A378603 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A033630(i) = A033630(j), for all i, j >= 1.
%C A378603 Restricted growth sequence transform of the ordered pair [A046523(n), A033630(n)].
%H A378603 Antti Karttunen, <a href="/A378603/b378603.txt">Table of n, a(n) for n = 1..100000</a>
%o A378603 (PARI)
%o A378603 up_to = 100000;
%o A378603 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 A378603 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A378603 v033630 = readvec("b033630_to.txt"); \\ Precomputed with A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
%o A378603 A033630(n) = v033630[n];
%o A378603 Aux378603(n) = [A046523(n), A033630(n)];
%o A378603 v378603 = rgs_transform(vector(up_to, n, Aux378603(n)));
%o A378603 A378603(n) = v378603[n];
%Y A378603 Cf. A046523, A033630, A101296.
%Y A378603 Cf. also A378601, A378602, A378604, A378605.
%K A378603 nonn
%O A378603 1,2
%A A378603 _Antti Karttunen_, Dec 01 2024