A331298 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001222(i) = A001222(j) and A061395(i) = A061395(j) for all i, j.

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

Offset: 1

Author

Antti Karttunen, Jan 18 2020

Keywords

• nonn

Comments

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

For all i, j:

A318891(i) = A318891(j) => a(i) = a(j),

a(i) = a(j) => A331297(i) = A331297(j) => A326846(i) = A326846(j),

a(i) = a(j) => A331281(i) = A331281(j),

a(i) = a(j) => A331282(i) = A331282(j).

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, A318891, A326846, A331281, A331282.

Cf. also A331297, 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])));
Aux331298(n) = [bigomega(n),A061395(n)];
v331298 = rgs_transform(vector(up_to, n, Aux331298(n)));
A331298(n) = v331298[n];