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A294936
Characteristic function for nondeficient numbers (A023196): a(n) = 1 if A001065(n) >= n, 0 otherwise.
12
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
OFFSET
1
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
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. 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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 12 2017
STATUS
approved