A323367 Lexicographically earliest such sequence a that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = 0 for odd primes, and f(n) = A323366(n) for any other number.

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, 26, 27, 3, 28, 26, 29, 3, 19, 3, 30, 31, 32, 3, 33, 34, 35, 36, 37, 3, 38, 39, 40, 41, 42, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 53, 54, 55, 56, 51, 3, 57, 58, 59, 3, 37, 60, 61, 62, 63, 3, 64, 65, 66, 56, 67, 65, 68, 3, 69, 70, 71, 3, 72, 3, 73, 47

Offset

1,2

Comments

Restricted growth sequence transform of function f, where f(n) = 0 for odd primes, and for any other number, f(n) = [A000035(n), A003557(n), A173557(n)].

For all i, j:

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

a(i) = a(j) => A007814(i) = A007814(j),

a(i) = a(j) => A322587(i) = A322587(j).

a(i) = a(j) => A323237(i) = A323237(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; };
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557
Aux323367(n) = if((n>2)&&isprime(n), 0, [(n%2), A003557(n), A173557(n)]);
v323367 = rgs_transform(vector(up_to, n, Aux323367(n)));
A323367(n) = v323367[n];

Crossrefs

Cf. A000035, A003557, A173557, A291756, A305801, A322587, A323237, A323366.

Cf. also A323369.

Sequence in context: A319346 A323369 A323400 * A323370 A323405 A353521

Adjacent sequences: A323364 A323365 A323366 * A323368 A323369 A323370

Keyword

nonn

Author

Antti Karttunen, Jan 12 2019

Status

approved