A294936 - OEIS

A294936

Characteristic function for nondeficient numbers (A023196): a(n) = 1 if A001065(n) >= n, 0 otherwise.

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

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OFFSET

COMMENTS

Differs from A210455 for the first time at n=70, and after that at n=836, 4030, 5830, 7192, 7912, 9272, etc., that is, at weird numbers, A006037.

Differs from A336835 for the first time at n=120. - Antti Karttunen, Apr 04 2022

LINKS

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

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 - A294934(n).

a(n) >= A210455(n).

a(n) >= A341619(n). - Antti Karttunen, Apr 04 2022

EXAMPLE

The proper divisors of 6 are 1, 2 and 3, and their sum is 6, and because 6 >= 6, a(6) = 1.

The proper divisors of 70 are 1, 2, 5, 7, 10, 14, and 35, and their sum is 74, and because 74 >= 70, a(70) = 1.

MATHEMATICA

Table[If[DivisorSigma[1, n]>=2n, 1, 0], {n, 120}] (* Harvey P. Dale, Mar 22 2020 *)

PROG

(PARI) a(n) = sigma(n, -1)>=2 \\ Felix Fröhlich, Nov 12 2017

CROSSREFS

Cf. A001065, A006037, A033880, A210455, A294887, A294934, A294935, A294937, A336835.

Cf. A023196 (positions of ones), A005100 (of zeros), A341620 (inverse Möbius transform), A294927 [= A341620(n)-a(n)], A341619.

Sequence in context: A044936 A133944 A210455 * A296210 A368990 A094912

Adjacent sequences: A294933 A294934 A294935 * A294937 A294938 A294939

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 12 2017

STATUS

approved