A336151 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A006530(i) = A006530(j), for all i, j >= 1.

1, 2, 3, 2, 4, 5, 6, 2, 3, 7, 8, 5, 9, 10, 7, 2, 11, 5, 12, 7, 10, 13, 14, 5, 4, 15, 3, 10, 16, 17, 18, 2, 13, 19, 10, 5, 20, 21, 15, 7, 22, 23, 24, 13, 7, 25, 26, 5, 6, 7, 19, 15, 27, 5, 13, 10, 21, 28, 29, 17, 30, 31, 10, 2, 15, 32, 33, 19, 25, 23, 34, 5, 35, 36, 7, 21, 13, 37, 38, 7, 3, 39, 40, 23, 19, 41, 28, 13, 42, 17, 15, 25, 31, 43, 21, 5, 44, 10, 13, 7, 45, 46, 47, 15, 23

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A001221(n), A006530(n)]. The first member of pair gives the number of distinct prime divisors of n, and the second member gives its largest prime factor.

For all i, j: A324400(i) = A324400(j) => A286621(i) = A286621(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A001221, A006530.

Cf. also A286621, A324400, A336150, A336152.

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; };
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
Aux336151(n) = [omega(n), A006530(n)];
v336151 = rgs_transform(vector(up_to, n, Aux336151(n)));
A336151(n) = v336151[n];