A359473 a(n) = 1 if the number of divisors of n is a power of 2, otherwise 0.

1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1

Offset

1

Links

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

Index entries for characteristic functions.

Index entries for sequences computed from exponents in factorization of n.

Formula

a(n) = A209229(A000005(n)).

a(n) = [A348341(n) == 0], where [ ] is the Iverson bracket.

A359472(n) <= a(n) <= A295316(n).

Sum_{k=1..n} a(k) ~ c * n, where c = A327839. - Amiram Eldar, Jan 05 2023

Multiplicative with a(p^e) = A209229(e+1). - Amiram Eldar, Oct 31 2025

Maple

f:= proc(n) local F;
  F:= ifactors(n)[2][.., 2];
  if andmap(t -> t = 2^padic:-ordp(t, 2), F +~ 1) then 1 else 0 fi
end proc:
map(f, [$1..200]); # Robert Israel, Oct 30 2025

Mathematica

a[n_] := If[IntegerQ@Log2[DivisorSigma[0, n]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jan 05 2023 *)

Prog

(PARI)
A209229(n) = (n && !bitand(n, n-1));
A359473(n) = A209229(numdiv(n));
(Python)
from sympy import factorint
def A359473(n): return int(all(map(lambda m:not((k:=m+1)&-k)^k, factorint(n).values()))) # Chai Wah Wu, Jan 04 2023

Crossrefs

Characteristic function of A036537, whose complement A162643 gives the positions of 0's.

Cf. A000005, A209229, A295316, A327839, A348341, A359472.

Sequence in context: A267773 A325321 A255887 * A181183 A295316 A014677

Adjacent sequences: A359470 A359471 A359472 * A359474 A359475 A359476

Keyword

nonn,mult

Author

Antti Karttunen, Jan 04 2023

Status

approved