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Characteristic function for abundant numbers (A005101): a(n) = 1 if A001065(n) > n, 0 otherwise.
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%I #10 Jul 25 2022 22:42:18

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A294937/b294937.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.

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

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

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

%t a[n_] := If[DivisorSigma[1, n] > 2*n, 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 25 2022 *)

%o (PARI) a(n) = sigma(n) > 2*n; \\ _Michel Marcus_, Jul 25 2022

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

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

%K nonn

%O 1

%A _Antti Karttunen_, Nov 12 2017