A323400 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = [A000035(n), A003557(n), A323363(n)] for all other numbers, except f(n) = 0 for odd primes.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 24, 26, 3, 27, 28, 29, 3, 30, 3, 31, 32, 33, 3, 34, 35, 36, 37, 38, 3, 39, 37, 40, 41, 42, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 48, 3, 51, 3, 52, 53, 54, 50, 55, 3, 56, 57, 58, 3, 59, 60, 61, 62, 63, 3, 64, 65, 66, 67, 68, 62, 69, 3, 70, 71, 72, 3, 73, 3

Offset: 1

Author

Antti Karttunen, Jan 15 2019

Keywords

• nonn

Comments

For all i, j:

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

a(i) = a(j) => A323369(i) = A323369(j),

a(i) = a(j) => A323401(i) = A323401(j).

Links

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

Crossrefs

Cf. A000035, A001615, A322588, A323363, A323369, A323400.

Cf. also A305801, A323370, A323372.

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; };
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(dA001615(n) = (n * sumdivmult(n, d, issquarefree(d)/d)); \\ From A001615
v323363 = DirInverse(vector(up_to,n,A001615(n)));
A323363(n) = v323363[n];
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
Aux323400(n) = if((n>2)&&isprime(n), 0, [(n%2), A003557(n), A323363(n)]);
v323400 = rgs_transform(vector(up_to, n, Aux323400(n)));
A323400(n) = v323400[n];