A329035 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329034(i) = A329034(j) for all i, j, where A329034 is the Möbius transform of A122111.
1, 1, 2, 1, 3, 1, 4, 5, 6, 2, 7, 2, 8, 3, 3, 5, 9, 10, 11, 3, 12, 4, 13, 5, 14, 7, 15, 4, 16, 3, 17, 10, 18, 8, 7, 5, 19, 9, 20, 21, 22, 4, 23, 7, 24, 11, 25, 21, 26, 27, 28, 8, 29, 10, 30, 27, 31, 13, 32, 1, 33, 16, 34, 5, 35, 7, 36, 9, 37, 38, 39, 40, 41, 17, 42, 11, 43, 8, 44, 27, 45, 19, 46, 6, 47, 22, 48, 49, 50, 10, 51, 13, 52, 23, 53, 54, 55, 56, 57, 58, 59, 9
Offset: 1
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PARI
up_to = 8192; 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; }; A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)}; A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n))); A329034(n) = sumdiv(n,d,moebius(n/d)*A122111(d)); v329035 = rgs_transform(vector(up_to, n, A329034(n))); A329035(n) = v329035[n];
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