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

1,2

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

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; };
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];

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.

Sequence in context: A369040 A328767 A319682 * A305793 A300245 A346488

Adjacent sequences: A329350 A329351 A329352 * A329354 A329355 A329356

Keyword

nonn

Author

Antti Karttunen, Nov 12 2019

Status

approved