A362077 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, 6, 8, 9, 10, 12, 15, 14, 16, 20, 18, 21, 22, 24, 28, 27, 30, 33, 26, 32, 5, 7, 11, 13, 17, 19, 23, 25, 34, 36, 40, 44, 39, 38, 42, 45, 48, 35, 46, 50, 51, 52, 54, 56, 60, 64, 66, 57, 58, 62, 68, 63, 69, 70, 72, 55, 74, 76, 75, 78, 81, 80, 65, 82, 84, 88, 92, 87, 86, 90, 96, 102, 93

Offset: 1

Author

Scott R. Shannon, Apr 08 2023

Keywords

• nonn

Comments

Other than the first three terms the only other primes in the first 500000 terms are the consecutive terms a(24)..a(30) = 5, 7, 11, 13, 17, 19, 23. It is unknown if more exist.

In the same range the fixed points are 1, 2, 3, 4, and 48559, although it is possible more exist.

Examples

			a(4) = 4 as Omega(a(3)) = A001222(3) = 1, and 4 is the smallest unused number that is a multiple of 1.
a(10) = 15 as Omega(a(9)) = A001222(12) = 3, and 15 is the smallest unused number that is a multiple of 3.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 200000 terms. The green line is a(n) = n.

Crossrefs

Cf. A001222, A362031, A354606, A000005, A124056, A342585.

Programs

Python

from sympy import primeomega
from itertools import count, islice
def A362077_gen(): # generator of terms
    a, b = {1,2}, 2
    yield from (1,2)
    while True:
        for b in count(p:=primeomega(b),p):
            if b not in a:
                yield b
                a.add(b)
                break
A362077_list = list(islice(A362077_gen(),20)) # Chai Wah Wu, Apr 11 2023