A323369 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) = A323368(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, 24, 26, 3, 27, 28, 29, 3, 30, 3, 31, 32, 22, 3, 33, 34, 35, 36, 37, 3, 38, 36, 39, 40, 41, 3, 42, 3, 30, 43, 44, 45, 46, 3, 47, 48, 46, 3, 49, 3, 50, 51, 52, 48, 53, 3, 54, 55, 56, 3, 57, 58, 59, 60, 61, 3, 62, 63, 42, 64, 46, 60, 65, 3, 66, 67, 68, 3, 69, 3

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), A048250(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) => A322588(i) = A322588(j),

a(i) = a(j) => A323238(i) = A323238(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); };
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
Aux323369(n) = if((n>2)&&isprime(n), 0, [(n%2), A003557(n), A048250(n)]);
v323369 = rgs_transform(vector(up_to, n, Aux323369(n)));
A323369(n) = v323369[n];

Crossrefs

Cf. A000035, A003557, A048250, A291750, A291751, A305801, A322588, A323238, A323368.

Cf. also A323367.

Sequence in context: A323371 A369447 A319346 * A323400 A323367 A323370

Adjacent sequences: A323366 A323367 A323368 * A323370 A323371 A323372

Keyword

nonn

Author

Antti Karttunen, Jan 12 2019

Status

approved