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A354921 Positions of odd terms in A182665.

%I A354921 #16 Jun 13 2022 19:32:29
%S A354921 2,3,4,5,7,8,9,11,12,13,16,17,19,21,23,25,27,28,29,30,31,32,35,37,39,
%T A354921 40,41,43,44,47,48,49,53,55,56,57,59,60,61,64,66,67,71,73,75,76,79,80,
%U A354921 81,83,85,89,90,92,93,97,99,101,102,103,104,105,107,108,109,111,113,117,119,120,121,124,125,126,127,128
%N A354921 Positions of odd terms in A182665.
%C A354921 Numbers k such that the parity of A344005(k) differs from the parity of k itself.
%o A354921 (PARI)
%o A354921 A354920(n) = forstep(x=n-1,0,-1,if(!((x*(x-1))%n),return(x%2)));
%o A354921 isA354921(n) = A354920(n);
%o A354921 (Python 3.8+)
%o A354921 from itertools import combinations, islice, count
%o A354921 from math import prod
%o A354921 from sympy import factorint
%o A354921 from sympy.ntheory.modular import crt
%o A354921 def A354921_gen(startvalue=2): # generator of terms >= startvalue
%o A354921     for n in count(max(startvalue,2)):
%o A354921         plist = tuple(p**q for p, q in factorint(n).items())
%o A354921         if len(plist) == 1 or (n-int(min(min(crt((m, n//m), (0, -1))[0], crt((n//m, m), (0, -1))[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))))) & 1:
%o A354921             yield n
%o A354921 A354921_list = list(islice(A354921_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A354921 Cf. A182665, A344005, A354920 (characteristic function), A354922 (complement).
%Y A354921 Cf. also A354919.
%K A354921 nonn
%O A354921 1,1
%A A354921 _Antti Karttunen_, Jun 12 2022