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A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.

%I A336148 #8 Jul 13 2020 07:54:33
%S A336148 1,2,3,2,4,5,6,2,7,8,9,5,10,11,12,2,13,14,15,8,16,17,18,5,19,20,21,11,
%T A336148 22,23,24,2,25,26,27,14,28,29,30,8,31,32,33,17,34,35,36,5,37,38,39,20,
%U A336148 40,41,25,11,42,43,44,23,45,46,47,2,48,49,50,26,51,32,52,14,53,54,34,29,55,56,57,8,58,59,60,32,61,62,63,17,64,65,30,35,66,67,68,5,69,70,71,38,72,73,74,20,75
%N A336148 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A336158(i) = A336158(j), for all i, j >= 1.
%C A336148 Restricted growth sequence transform of the ordered pair [A278221(n), A336158(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A000265(n))].
%C A336148 For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).
%H A336148 Antti Karttunen, <a href="/A336148/b336148.txt">Table of n, a(n) for n = 1..65537</a>
%o A336148 (PARI)
%o A336148 up_to = 65537;
%o A336148 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 A336148 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A336148 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
%o A336148 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A336148 A278221(n) = A046523(A122111(n));
%o A336148 A000265(n) = (n>>valuation(n,2));
%o A336148 A336158(n) = A046523(A000265(n));
%o A336148 Aux336148(n) = [A278221(n),A336158(n)];
%o A336148 v336148 = rgs_transform(vector(up_to, n, Aux336148(n)));
%o A336148 A336148(n) = v336148[n];
%Y A336148 Cf. A000265, A046523, A064989, A122111, A278221, A336158.
%Y A336148 Cf. also A286621, A318890, A324400, A336146, A336149, A336159.
%K A336148 nonn
%O A336148 1,2
%A A336148 _Antti Karttunen_, Jul 12 2020