A294934 Characteristic function for deficient numbers (A005100): a(n) = 1 if A001065(n) < n, 0 otherwise.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Index entries for sequences related to sums of divisors.

Formula

a(n) = 1 if A033879(n) > 0, 0 otherwise.

a(n) = 1 - A294936(n).

a(n) = 1 - sign(floor(sigma(n)/(2*n))), where sigma is the sum of the divisors of n (A000203). - Wesley Ivan Hurt, Oct 01 2020

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A318172. - Amiram Eldar, Jul 25 2022

Mathematica

Table[1 - Sign[Floor[DivisorSigma[1, n]/(2 n)]], {n, 100}] (* Wesley Ivan Hurt, Oct 02 2020 *)

Crossrefs

Cf. A001065, A033879, A294935, A294936, A294937, A318172.

Cf. A005100 (positions of 1's), A023196 (of 0's).

Cf. A000203 (sigma).

Sequence in context: A071040 A336834 A356173 * A360128 A174340 A300294

Adjacent sequences: A294931 A294932 A294933 * A294935 A294936 A294937

Keyword

nonn,easy

Author

Antti Karttunen, Nov 12 2017

Status

approved