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A354919 Positions of odd terms in A344005.

%I A354919 #14 Jun 13 2022 03:02:18
%S A354919 1,2,4,8,12,15,16,28,30,32,33,40,44,45,48,51,56,60,63,64,65,66,69,76,
%T A354919 77,80,87,90,91,92,95,102,104,108,115,120,123,124,126,128,130,132,138,
%U A354919 141,143,144,145,153,154,159,161,172,174,175,177,180,182,184,187,188,189,190,192,195,204,207,213,215,221,224
%N A354919 Positions of odd terms in A344005.
%C A354919 Numbers k such that the parity of A182665(k) differs from the parity of k itself.
%o A354919 (PARI)
%o A354919 A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));
%o A354919 isA354919(n) = A354918(n);
%o A354919 (Python 3.8+)
%o A354919 from itertools import combinations, islice, count
%o A354919 from math import prod
%o A354919 from sympy import factorint
%o A354919 from sympy.ntheory.modular import crt
%o A354919 def A354919_gen(startvalue=1): # generator of terms >= startvalue
%o A354919     if startvalue <= 1:
%o A354919         yield 1
%o A354919     for n in count(max(startvalue,2)):
%o A354919         plist = tuple(p**q for p, q in factorint(n).items())
%o A354919         if len(plist) == 1:
%o A354919             if (n-1) & 1: yield n
%o A354919         elif 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 A354919             yield n
%o A354919 A354919_list = list(islice(A354919_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A354919 Cf. A002378, A182665, A344005, A354918 (characteristic function).
%Y A354919 Cf. also A354921.
%K A354919 nonn
%O A354919 1,2
%A A354919 _Antti Karttunen_, Jun 12 2022