OFFSET
1,2
COMMENTS
This sequence can be generalized easily: for any i > 1 and j > 1 such that gcd(i, j)=1:
- let f_i_j be the lexicographically earliest sequence of distinct positive numbers such that, for any n > 0, f_i_j(i*n) = j*f_i_j(n),
- in particular, f_2_3 = a (this sequence),
- if n is the k-th positive number not divisible by i and m the k-th positive number not divisible by j, then f_i_j(n) = m, and for any x >= 0, f_i_j(n*i^x) = m*j^x,
- a(n) is divisible by j^x iff n is divisible by i^x,
- f_i_j is a permutation of the natural numbers, with inverse f_j_i,
- f_i_j(1) = 1.
See A294371 for the inverse of this sequence.
Apparently, a(1) = 1 and a(6) = 6 are the only fixed points of this sequence.
LINKS
EXAMPLE
a(1) = 1 is suitable, and a(2^i) = 3^i for any i >= 0.
a(2) = 3 * a(1) = 3.
a(3) = 2 is suitable, and a(3*2^i) = 2*3^i for any i >= 0.
a(4) = 3 * a(2) = 9.
a(5) = 4 is suitable, and a(5*2^i) = 4*3^i for any i >= 0.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Rémy Sigrist, Oct 29 2017
STATUS
approved