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A351955 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328571(A108951(i)) = A328571(A108951(j)) for all i, j >= 1.

%I A351955 #18 Apr 04 2022 15:25:49
%S A351955 1,2,3,2,4,3,5,6,7,4,8,3,9,5,4,6,10,7,11,4,5,8,12,7,13,9,14,5,15,13,
%T A351955 16,17,8,10,18,7,19,11,9,13,20,18,21,8,13,12,22,7,23,13,10,9,24,14,25,
%U A351955 5,11,15,26,13,27,16,18,17,28,8,29,10,12,18,30,31,32,19,33,11,25,9,34,13,31,20,35,18,36,21,15,8
%N A351955 Lexicographically earliest infinite sequence such that a(i) = a(j) => A328571(A108951(i)) = A328571(A108951(j)) for all i, j >= 1.
%C A351955 Restricted growth sequence transform of A346091, or equally, of A346093.
%C A351955 For all i, j:
%C A351955   a(i) = a(j) => A006530(i) = A006530(j) [equally, A061395(i) = A061395(j)],
%C A351955   a(i) = a(j) => A329040(i) = A329040(j) => A351956(i) = A351956(j),
%C A351955   a(i) = a(j) => A329343(i) = A329343(j).
%C A351955 Interestingly, some of the rays in the scatter plot appear to be cut to discontinuous segments.
%H A351955 Antti Karttunen, <a href="/A351955/b351955.txt">Table of n, a(n) for n = 1..65537</a>
%H A351955 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A351955 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A351955 (PARI)
%o A351955 up_to = 65537;
%o A351955 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 A351955 A002110(n) = prod(i=1,n,prime(i));
%o A351955 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^f[i, 2]) };
%o A351955 A328571(n) = { my(m=1, p=2); while(n, m *= (p^!!(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A351955 A346091(n) = A328571(A108951(n));
%o A351955 v351955 = rgs_transform(vector(up_to, n, A346091(n)));
%o A351955 A351955(n) = v351955[n];
%Y A351955 Cf. A108951, A328571, A346091, A346093.
%Y A351955 Cf. also A006530, A061395, A329040, A329343, A351956, and A286621, A329045, A329345, A344594.
%K A351955 nonn,look
%O A351955 1,2
%A A351955 _Antti Karttunen_, Apr 03 2022