A374032 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278226(A374031(i)) = A278226(A374031(j)), for all i, j >= 1.
1, 2, 2, 2, 2, 2, 2, 3, 4, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 4, 3, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 5, 4, 2, 4, 2, 2, 2, 4, 6, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 4, 4, 2, 2, 3, 3, 7, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 8, 2, 2, 2, 3, 2, 2, 2, 4, 2, 4, 3, 2, 2, 9, 4, 3, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6
Offset: 1
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PARI
up_to = 100000; 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; }; A002110(n) = prod(i=1,n,prime(i)); A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); }; A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); }; A278226(n) = A046523(A276086(n)); 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])); A374031(n) = gcd(A276085(n), A328768(n)); v374032 = rgs_transform(vector(up_to, n, A278226(A374031(n)))); A374032(n) = v374032[n];
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