A383277 The number of divisors d of n for which A034444(d)*d is equal to n.

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

Offset

1

Comments

The number of these divisors is either 0 or 1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

H. L. Abbott and M. V. Subbarao, On the Distribution of the Sequence {nd*(n)}, Canadian Mathematical Bulletin , Vol. 32 , No. 1 (1989), pp. 105-108.

Formula

a(n) = 1 if either A007814(n) = A005087(n) or A007814(n) > A005087(n) + 1, and 0 otherwise.

Mathematica

a[n_] := DivisorSum[n, 1 &, # * 2^PrimeNu[#] == n &]; Array[a, 100]
(* second program: *)
a[n_] := Module[{e = IntegerExponent[n, 2], w}, w = PrimeNu[n/2^e]; If[e > w + 1 || e == w, 1, 0]]; Array[a, 100]

Prog

(PARI) a(n) = sumdiv(n, d, (1 << omega(d)) * d == n);
(PARI) a(n) = {my(e = valuation(n, 2), w = omega(n >> e)); e > w + 1 || e == w; }

Crossrefs

Characteristic function of A383276.

First differences of A383278.

The unitary analog of A327166.

Cf. A005087, A007814, A034444, A383279.

Sequence in context: A121559 A004641 A266441 * A266672 A266070 A262855

Adjacent sequences: A383274 A383275 A383276 * A383278 A383279 A383280

Keyword

nonn,easy

Author

Amiram Eldar, Apr 21 2025

Status

approved