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

1,2

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

Prog

(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(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A001615(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];

Crossrefs

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

Cf. also A305801, A323370, A323372.

Sequence in context: A369447 A319346 A323369 * A323367 A323370 A323405

Adjacent sequences: A323397 A323398 A323399 * A323401 A323402 A323403

Keyword

nonn

Author

Antti Karttunen, Jan 15 2019

Status

approved