A331297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A263297(i) = A263297(j) and A325225(i) = A325225(j) for all i, j.

1, 2, 3, 3, 4, 5, 6, 4, 5, 7, 8, 7, 9, 10, 7, 6, 11, 7, 12, 13, 10, 14, 15, 10, 7, 16, 7, 17, 18, 13, 19, 8, 14, 20, 10, 10, 21, 22, 16, 17, 23, 17, 24, 25, 13, 26, 27, 14, 10, 13, 20, 28, 29, 10, 14, 30, 22, 31, 32, 17, 33, 34, 17, 9, 16, 25, 35, 36, 26, 17, 37, 14, 38, 39, 13, 40, 14, 28, 41, 25, 10, 42, 43, 30, 20, 44, 31, 45, 46, 17, 16, 47, 34, 48, 22, 16, 49, 17, 25, 17

Offset: 1

Author

Antti Karttunen, Jan 18 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the unordered pair [A001222(n), A061395(n)].

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001222, A061395, A263297, A325225, A331170, A331298, A331299.

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; };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
Aux331297(n) = { my(a=bigomega(n),b=A061395(n)); [min(a,b),max(a,b)]; };
Aux331297(n) = Set([bigomega(n),A061395(n)]); \\ Alternatively.
v331297 = rgs_transform(vector(up_to, n, Aux331297(n)));
A331297(n) = v331297[n];

Formula

For all i, j:

A331170(i) = A331170(j) => a(i) = a(j),

A331298(i) = A331298(j) => a(i) = a(j),

A331299(i) = A331299(j) => a(i) = a(j),

a(i) = a(j) => A326846(i) = A326846(j).