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A373982 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A328768(i)) = A278226(A328768(j)), for all i, j >= 0.

%I A373982 #10 Jun 26 2024 09:32:22
%S A373982 1,1,2,2,3,2,4,2,3,3,5,2,6,2,7,8,4,2,9,2,7,10,11,2,10,3,5,12,13,2,11,
%T A373982 2,10,14,15,16,8,2,10,17,18,2,19,2,20,21,22,2,23,3,24,10,25,2,20,26,
%U A373982 17,27,28,2,29,2,7,24,16,29,30,2,20,22,31,2,32,2,33,19,34,35,36,2,11,4,37,2,22,29,11,25,38,2,33,39,17,10,40,41,10,2,42,43,20
%N A373982 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A328768(i)) = A278226(A328768(j)), for all i, j >= 0.
%C A373982 Restricted growth sequence transform of A278226(A328768(n)).
%C A373982 For all i, j >= 1:
%C A373982   A305800(i) = A305800(j) => A373983(i) = A373983(j) => a(i) = a(j).
%C A373982 For all i, j >= 0: a(i) = a(j) => A328771(i) = A328771(j).
%H A373982 Antti Karttunen, <a href="/A373982/b373982.txt">Table of n, a(n) for n = 0..100000</a>
%H A373982 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A373982 (PARI)
%o A373982 up_to = 100000;
%o A373982 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 A373982 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A373982 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A373982 A278226(n) = A046523(A276086(n));
%o A373982 A002110(n) = prod(i=1,n,prime(i));
%o A373982 A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
%o A373982 v373982 = rgs_transform(vector(1+up_to, n, A278226(A328768(n-1))));
%o A373982 A373982(n) = v373982[1+n];
%Y A373982 Cf. A002110, A046523, A276085, A276086, A278226, A328768, A373983.
%Y A373982 Cf. also A329045.
%K A373982 nonn
%O A373982 0,3
%A A373982 _Antti Karttunen_, Jun 25 2024