A329353 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329352(i) = A329352(j) for all i, j.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 12, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 7, 34, 35, 25, 2, 36, 27, 37, 38, 39, 2, 40, 2, 41, 42, 43, 44, 45, 2, 46, 47, 48, 2, 49, 2, 50, 51, 52, 53, 54, 2, 55, 56, 57, 2, 58, 59, 60, 61, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71, 72, 2, 73, 2, 49, 74

Offset: 1

Author

Antti Karttunen, Nov 12 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of A329352.

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j),

a(i) = a(j) => A069359(i) = A069359(j).

Links

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

Crossrefs

Cf. A010051, A019565, A069359, A305800, A329352.

Cf. also A329351.

Differs from A319682 for the first time at n=254, where a(254)=123, while A319682(254)=184.

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; };
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A329352(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A019565(d))); (m); };
v329353 = rgs_transform(vector(up_to, n, A329352(n)));
A329353(n) = v329353[n];