A324399 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = A000265(n) for all other numbers, except that f(n) = 0 if n is an odd prime, and f(1) = -1 and f(2) = -2.

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

Offset: 1

Author

Antti Karttunen, Mar 01 2019

Keywords

• nonn

Comments

For all i, j:

A324401(i) = A324401(j) => a(i) = a(j).

Links

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

Crossrefs

Cf. A000040, A000265, A003602, A322809, A324401.

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; };
A000265(n) = (n/2^valuation(n, 2));
Aux324399(n) = if(n<3,-n,if(isprime(n),0,A000265(n)));
v324399 = rgs_transform(vector(up_to, n, Aux324399(n)));
A324399(n) = v324399[n];