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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)).
2
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, 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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Apr 08 2023
STATUS
approved