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A355000 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A327858(i) = A327858(j) for all i, j >= 1.

%I A355000 #10 Jul 20 2022 18:43:29
%S A355000 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,8,2,12,13,7,2,14,15,16,5,8,2,17,
%T A355000 2,18,19,7,20,21,2,22,10,14,2,17,2,12,12,23,2,24,25,26,13,27,2,14,10,
%U A355000 14,10,7,2,28,2,9,12,29,30,17,2,12,10,17,2,31,2,9,32,32,30,17,2,33,34,7,2,28,10,16,10,35,2,28,10,12,10,36,20,37,2,27,26,38,2,39,2,14,17
%N A355000 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A327858(i) = A327858(j) for all i, j >= 1.
%C A355000 Restricted growth sequence transform of the ordered pair [A046523(n), A327858(n)].
%C A355000 For all i, j: A351235(i) = A351235(j) => a(i) = a(j).
%H A355000 Antti Karttunen, <a href="/A355000/b355000.txt">Table of n, a(n) for n = 1..65537</a>
%H A355000 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A355000 (PARI)
%o A355000 up_to = 65537;
%o A355000 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 A355000 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A355000 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A355000 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A355000 A327858(n) = gcd(A003415(n),A276086(n));
%o A355000 Aux355000(n) = [A046523(n), A327858(n)];
%o A355000 v355000 = rgs_transform(vector(up_to,n,Aux355000(n)));
%o A355000 A355000(n) = v355000[n];
%Y A355000 Cf. A003415, A046523, A276086, A327858, A351235.
%Y A355000 Cf. also A355830, A355831, A355836.
%K A355000 nonn,easy
%O A355000 1,2
%A A355000 _Antti Karttunen_, Jul 19 2022