A354764 Squarefree kernel of A090252(n) (cf. A007947).

1, 2, 3, 5, 2, 7, 3, 11, 13, 17, 2, 19, 23, 5, 21, 29, 31, 37, 41, 43, 47, 53, 2, 59, 61, 67, 71, 73, 55, 79, 3, 7, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 26, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 85, 11, 223, 227, 57, 229, 161, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Author

N. J. A. Sloane, Jun 18 2022

Keywords

• nonn

Crossrefs

Cf. A007947, A090252.

Programs

Python

from itertools import count, islice
from math import prod, gcd, lcm
from collections import deque
from sympy import primefactors
def A354764_gen(): # generator of terms
    aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
    yield 1
    while True:
        for m in count(c):
            if m not in aset and gcd(m,b) == 1:
                yield prod(primefactors(m))
                aset.add(m)
                aqueue.append(m)
                if f: aqueue.popleft()
                b = lcm(*aqueue)
                f = not f
                while c in aset:
                    c += 1
                break
A354764_list = list(islice(A354764_gen(),20)) # Chai Wah Wu, Jun 18 2022