A354919 - OEIS

%I #14 Jun 13 2022 03:02:18

%S 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 77,80,87,90,91,92,95,102,104,108,115,120,123,124,126,128,130,132,138,

%U 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 Positions of odd terms in A344005.

%C Numbers k such that the parity of A182665(k) differs from the parity of k itself.

%o (PARI)

%o A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));

%o isA354919(n) = A354918(n);

%o (Python 3.8+)

%o from itertools import combinations, islice, count

%o from math import prod

%o from sympy import factorint

%o from sympy.ntheory.modular import crt

%o def A354919_gen(startvalue=1): # generator of terms >= startvalue

%o     if startvalue <= 1:

%o         yield 1

%o     for n in count(max(startvalue,2)):

%o         plist = tuple(p**q for p, q in factorint(n).items())

%o         if len(plist) == 1:

%o             if (n-1) & 1: yield n

%o         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             yield n

%o A354919_list = list(islice(A354919_gen(),40)) # _Chai Wah Wu_, Jun 12 2022

%Y Cf. A002378, A182665, A344005, A354918 (characteristic function).

%Y Cf. also A354921.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 12 2022