A339811 Lexicographically earliest infinite sequence such that a(i) = a(j) => A339810(i) = A339810(j), for all i, j >= 1.

1, 2, 2, 3, 3, 4, 2, 4, 2, 5, 2, 4, 4, 6, 4, 4, 4, 7, 4, 6, 2, 5, 4, 5, 5, 8, 2, 9, 2, 4, 2, 5, 3, 4, 4, 10, 4, 4, 2, 11, 2, 12, 4, 4, 5, 11, 2, 4, 8, 5, 2, 13, 2, 14, 2, 15, 8, 8, 4, 16, 2, 4, 2, 17, 4, 5, 2, 11, 3, 4, 2, 4, 4, 5, 4, 18, 4, 6, 4, 8, 2, 19, 4, 4, 8, 5, 4, 11, 2, 8, 2, 12, 4, 4, 4, 11, 20, 4, 5, 19, 3, 4, 4, 4, 4

Offset: 1

Author

Antti Karttunen, Dec 18 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A019565, A046523, A339809, A339810, A339812.

Programs

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; };
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A339810(n) = A046523(A019565(n)-1);
v339811 = rgs_transform(vector(up_to, n, A339810(n)));
A339811(n) = v339811[n];