A324203 Lexicographically earliest sequence such that a(i) = a(j) => A324202(i) = A324202(j) for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 8, 2, 9, 4, 4, 2, 10, 3, 4, 5, 9, 2, 11, 2, 12, 4, 4, 4, 13, 2, 4, 4, 14, 2, 11, 2, 9, 6, 4, 2, 15, 3, 8, 4, 9, 2, 16, 4, 17, 4, 4, 2, 18, 2, 4, 9, 19, 4, 11, 2, 9, 4, 11, 2, 20, 2, 4, 8, 9, 4, 11, 2, 21, 7, 4, 2, 20, 4, 4, 4, 17, 2, 22, 4, 9, 4, 4, 4, 23, 2, 8, 9, 24, 2, 11, 2, 17, 11

Offset: 1

Author

Antti Karttunen, Feb 19 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of A324202.

For all i, j:

a(i) = a(j) => A324190(i) = A324190(j),

a(i) = a(j) => A324191(i) = A324191(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A300827, A324181, A324190, A324191, A324202.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A324202(n) = A046523(factorback(apply(x -> prime(1+x),apply(A297167, select(d -> d>1,divisors(n))))));
v324203 = rgs_transform(vector(up_to, n, A324202(n)));
A324203(n) = v324203[n];