A336150 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A020639(i) = A020639(j), for all i, j >= 1.

1, 2, 3, 2, 4, 5, 6, 2, 3, 5, 7, 5, 8, 5, 9, 2, 10, 5, 11, 5, 9, 5, 12, 5, 4, 5, 3, 5, 13, 14, 15, 2, 9, 5, 16, 5, 17, 5, 9, 5, 18, 14, 19, 5, 9, 5, 20, 5, 6, 5, 9, 5, 21, 5, 16, 5, 9, 5, 22, 14, 23, 5, 9, 2, 16, 14, 24, 5, 9, 14, 25, 5, 26, 5, 9, 5, 27, 14, 28, 5, 3, 5, 29, 14, 16, 5, 9, 5, 30, 14, 27, 5, 9, 5, 16, 5, 31, 5, 9, 5, 32, 14, 33, 5, 34

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A001221(n), A020639(n)]. The first member of pair gives the number of distinct prime divisors of n, and the second member gives its smallest prime factor.

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

Links

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

Crossrefs

Cf. A001221, A020639.

Cf. also A324400, A336151, 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; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
Aux336150(n) = [omega(n), A020639(n)];
v336150 = rgs_transform(vector(up_to, n, Aux336150(n)));
A336150(n) = v336150[n];