A322592 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) = A289625(n) for any other number.

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

Offset

1,3

Comments

For all i, j:

a(i) = a(j) => A034380(i) = A034380(j),

a(i) = a(j) => A104194(i) = A104194(j),

a(i) = a(j) => A290084(i) = A290084(j).

Links

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

Prog

(PARI)
default(parisizemax, 2^31);
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; };
A289625(n) = { my(m=1, p=2, v=znstar(n)[2]); for(i=1, length(v), m *= p^v[i]; p = nextprime(p+1)); (m); };
Aux322592(n) = if((n>2)&&isprime(n), 0, A289625(n));
v322592 = rgs_transform(vector(up_to, n, Aux322592(n)));
A322592(n) = v322592[n];
for(n=1, up_to, write("b322592.txt", n, " ", A322592(n)));

Crossrefs

Cf. A289625, A289626, A322587, A322588, A322589, A322591.

Sequence in context: A167530 A205789 A029208 * A329896 A366262 A303779

Adjacent sequences: A322589 A322590 A322591 * A322593 A322594 A322595

Keyword

nonn

Author

Antti Karttunen, Dec 18 2018

Status

approved