A374478 Lexicographically earliest infinite sequence such that a(i) = a(j) => A348717(i) = A348717(j) and A364255(i) = A364255(j), for all i, j >= 1.
1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 11, 12, 13, 5, 14, 5, 15, 16, 17, 5, 18, 19, 20, 21, 22, 5, 23, 5, 24, 25, 26, 27, 28, 5, 29, 30, 31, 5, 32, 5, 33, 34, 35, 5, 36, 37, 38, 39, 40, 5, 41, 42, 43, 44, 45, 5, 46, 5, 47, 48, 49, 50, 51, 5, 52, 53, 54, 5, 55, 5, 56, 57, 58, 59, 60, 5, 61, 62, 63, 5, 64, 65, 66, 67, 68, 5, 69, 70, 71, 72, 73, 39, 74, 5, 75, 76, 77, 5
Offset: 1
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PARI
up_to = 65537; 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; }; A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f)); A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p)); A364255(n) = gcd(n, A163511(n)); Aux374478(n) = [A348717(n), A364255(n)]; v374478 = rgs_transform(vector(up_to, n, Aux374478(n))); A374478(n) = v374478[n];
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