A323374 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A323373(n) for all other numbers, except f(p) = -(p mod 2) for primes p.

1, 2, 3, 4, 3, 4, 3, 5, 6, 5, 3, 5, 3, 7, 8, 9, 3, 7, 3, 9, 10, 11, 3, 9, 12, 13, 14, 15, 3, 9, 3, 16, 12, 16, 17, 13, 3, 18, 17, 16, 3, 13, 3, 19, 20, 21, 3, 16, 22, 19, 23, 24, 3, 18, 25, 26, 27, 28, 3, 16, 3, 29, 30, 31, 32, 33, 3, 31, 34, 24, 3, 26, 3, 35, 25, 36, 37, 26, 3, 31, 38, 39, 3, 26, 40, 41, 42, 39, 3, 26, 43, 44, 37, 45, 46, 31, 3, 41, 47, 39, 3, 31, 3, 48

Offset: 1

Author

Antti Karttunen, Jan 13 2019

Keywords

• nonn

Comments

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j),

a(i) = a(j) => A039651(i) = A039651(j).

Links

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

Crossrefs

Cf. A039651, A049559, A160595, A323373.

Cf. also A322587, A322592, A323405.

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; };
A049559(n) = gcd(eulerphi(n), n-1);
A160595(n) = if(1==n, n, numerator(eulerphi(n)/(n-1)));
Aux323374(n) = if(isprime(n),-(n%2),[A049559(n), A160595(n)]);
v323374 = rgs_transform(vector(up_to, n, Aux323374(n)));
A323374(n) = v323374[n];