A362178 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of omega(a(n-1)).

1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 14, 16, 11, 13, 15, 18, 20, 22, 24, 26, 28, 30, 21, 32, 17, 19, 23, 25, 27, 29, 31, 33, 34, 36, 38, 40, 42, 39, 44, 46, 48, 50, 52, 54, 56, 58, 60, 45, 62, 64, 35, 66, 51, 68, 70, 57, 72, 74, 76, 78, 63, 80, 82, 84, 69, 86, 88, 90, 75, 92, 94, 96, 98, 100

Offset

1,2

Comments

Unlike A362077 numerous primes appear in the sequence; in the first 500000 terms there are seventy-four in total. In the same range there are twelve fixed points, the last being 57. It is unknown whether more exist.

Links

Table of n, a(n) for n=1..75.

Scott R. Shannon, Image of the first 500000 terms. The green line is a(n) = n.

Example

a(5) = 5 as omega(a(4)) = A001221(4) = 1, and 5 is the smallest unused number that is a multiple of 1.
a(7) = 8 as omega(a(6)) = A001221(6) = 2, and 8 is the smallest unused number that is a multiple of 2.

Prog

(Python)
from itertools import count, islice
from sympy import primenu
def A362178_gen(): # generator of terms
    a, b = {1, 2}, 2
    yield from (1, 2)
    while True:
        for b in count(p:=primenu(b), p):
            if b not in a:
                yield b
                a.add(b)
                break
A362178_list = list(islice(A362178_gen(), 20)) # Chai Wah Wu, Apr 12 2023

Crossrefs

Cf. A001221, A362077, A362031, A354606, A000005, A124056, A342585.

Sequence in context: A117332 A368578 A242704 * A358122 A334111 A243571

Adjacent sequences: A362175 A362176 A362177 * A362179 A362180 A362181

Keyword

nonn

Author

Scott R. Shannon, Apr 11 2023

Status

approved