A350064 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350062(i) = A350062(j), for all i, j >= 1.

1, 2, 3, 3, 4, 3, 5, 3, 6, 4, 7, 3, 8, 3, 6, 6, 9, 3, 10, 3, 11, 6, 12, 3, 11, 6, 6, 6, 13, 6, 14, 3, 6, 6, 11, 5, 15, 3, 16, 6, 17, 3, 18, 3, 6, 19, 20, 3, 19, 4, 16, 3, 21, 3, 22, 3, 16, 11, 23, 3, 24, 6, 6, 11, 11, 6, 25, 6, 6, 3, 26, 6, 27, 6, 6, 6, 19, 6, 28, 3, 16, 6, 29, 11, 30, 16, 31, 19, 32, 11, 33, 6, 30, 30, 30

Offset: 1

Author

Antti Karttunen, Jan 29 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of A350062.

For all i, j >= 1: a(i) = a(j) => A324105(i) = A324105(j).

For all i, j >= 2:

a(i) = a(j) => A324119(i) = A324119(j),

a(i) = a(j) => A342655(i) = A342655(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A046523, A156552, A350062, A350065.

Cf. also A286621, A324105, A324119, A342655.

Programs

PARI

up_to = 3000;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A350062(n) = if(1==n,0,A046523(A156552(n)));
v350064 = rgs_transform(vector(up_to, n, A350062(n)));
A350064(n) = v350064[n];