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

%I A354764 #10 Jun 19 2022 02:16:30
%S A354764 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,
%T A354764 71,73,55,79,3,7,83,89,97,101,103,107,109,113,127,131,137,139,149,151,
%U A354764 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
%N A354764 Squarefree kernel of A090252(n) (cf. A007947).
%o A354764 (Python)
%o A354764 from itertools import count, islice
%o A354764 from math import prod, gcd, lcm
%o A354764 from collections import deque
%o A354764 from sympy import primefactors
%o A354764 def A354764_gen(): # generator of terms
%o A354764     aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
%o A354764     yield 1
%o A354764     while True:
%o A354764         for m in count(c):
%o A354764             if m not in aset and gcd(m,b) == 1:
%o A354764                 yield prod(primefactors(m))
%o A354764                 aset.add(m)
%o A354764                 aqueue.append(m)
%o A354764                 if f: aqueue.popleft()
%o A354764                 b = lcm(*aqueue)
%o A354764                 f = not f
%o A354764                 while c in aset:
%o A354764                     c += 1
%o A354764                 break
%o A354764 A354764_list = list(islice(A354764_gen(),20)) # _Chai Wah Wu_, Jun 18 2022
%Y A354764 Cf. A007947, A090252.
%K A354764 nonn
%O A354764 1,2
%A A354764 _N. J. A. Sloane_, Jun 18 2022