A361465 - OEIS

%I #15 Mar 21 2023 09:22:56

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

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

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

%N a(n) = 1 if A017665(n) [the numerator of the sum of the reciprocals of the divisors of n] is a power of 2, otherwise 0.

%H Antti Karttunen, <a href="/A361465/b361465.txt">Table of n, a(n) for n = 1..100000</a>

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A209229(A017665(n)).

%F If a(x) = a(y) = gcd(x, y) = 1, then also a(x*y) = 1.

%t pow[n_] := If[n == 2^IntegerExponent[n, 2], 1, 0];

%t a[n_] := pow[Numerator[DivisorSigma[-1, n]]]; Array[a, 100] (* _Amiram Eldar_, Mar 20 2023 *)

%o (PARI)

%o A017665(n) = numerator(sigma(n)/n);

%o A209229(n) = (n && !bitand(n,n-1));

%o A361465(n) = A209229(A017665(n));

%Y Characteristic function of A043305.

%Y Cf. A017665, A209229, A355943 [= A000035(n)*a(n)], A361466 [= a(A003961(n))].

%K nonn

%O 1

%A _Antti Karttunen_, Mar 20 2023