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

1,2

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.

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.

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A143896 A160719 A263079 * A085451 A240911 A064150

Adjacent sequences: A362074 A362075 A362076 * A362078 A362079 A362080

Keyword

nonn

Author

Scott R. Shannon, Apr 08 2023

Status

approved