A294937 Characteristic function for abundant numbers (A005101): a(n) = 1 if A001065(n) > n, 0 otherwise.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for characteristic functions.

Index entries for sequences related to sums of divisors.

Formula

a(n) = 1 if A033880(n) > 0, 0 otherwise.

a(n) = 1 - A294935(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A302991. - Amiram Eldar, Jul 25 2022

Mathematica

a[n_] := If[DivisorSigma[1, n] > 2*n, 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 25 2022 *)

Prog

(PARI) a(n) = sigma(n) > 2*n; \\ Michel Marcus, Jul 25 2022

Crossrefs

Cf. A001065, A033880, A294934, A294935, A294936, A302991.

Cf. A005101 (positions of ones), A263837 (of zeros).

Sequence in context: A294930 A353472 A359475 * A363131 A355447 A045701

Adjacent sequences: A294934 A294935 A294936 * A294938 A294939 A294940

Keyword

nonn

Author

Antti Karttunen, Nov 12 2017

Status

approved