A361465 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.

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, 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, 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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

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

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

Mathematica

pow[n_] := If[n == 2^IntegerExponent[n, 2], 1, 0];
a[n_] := pow[Numerator[DivisorSigma[-1, n]]]; Array[a, 100] (* Amiram Eldar, Mar 20 2023 *)

Prog

(PARI)
A017665(n) = numerator(sigma(n)/n);
A209229(n) = (n && !bitand(n, n-1));
A361465(n) = A209229(A017665(n));

Crossrefs

Characteristic function of A043305.

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

Sequence in context: A188467 A039983 A152490 * A145273 A295892 A120522

Adjacent sequences: A361462 A361463 A361464 * A361466 A361467 A361468

Keyword

nonn

Author

Antti Karttunen, Mar 20 2023

Status

approved