A378449 - OEIS

%I #14 Dec 03 2024 11:45:36

%S 0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0

%N Characteristic function of A083209: a(n) = 1 if there is exactly one subset of the divisors of n such that the complement has the same sum, otherwise 0.

%H Antti Karttunen, <a href="/A378449/b378449.txt">Table of n, a(n) for n = 1..101632</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = [A083206(n) = 1], where [ ] is the Iverson bracket.

%F a(n) <= A378598(n) <= A179527(n).

%o (PARI)

%o A083206(n) = { my(p=1); fordiv(n, d, p *= ('x^d + 'x^-d)); (polcoeff(p, 0)/2); };

%o A378449(n) = (1==A083206(n));

%Y Characteristic function of A083209.

%Y Cf. A083206, A179527, A378448, A378598.

%K nonn,changed

%O 1

%A _Antti Karttunen_, Nov 28 2024