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A256562 Number of deficient numbers <= n. 1

%I

%S 1,2,3,4,5,5,6,7,8,9,10,10,11,12,13,14,15,15,16,16,17,18,19,19,20,21,

%T 22,22,23,23,24,25,26,27,28,28,29,30,31,31,32,32,33,34,35,36,37,37,38,

%U 39,40,41,42,42,43,43,44,45,46,46,47,48,49,50,51,51,52,53

%N Number of deficient numbers <= n.

%H Amiram Eldar, <a href="/A256562/b256562.txt">Table of n, a(n) for n = 1..10000</a>

%H Marc Del├ęglise, <a href="http://projecteuclid.org/euclid.em/1048515661">Bounds for the density of abundant integers</a>, Experiment. Math. Volume 7, Issue 2 (1998), 137-143.

%H Charles R. Wall, Phillip L. Crews and Donald B. Johnson, <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0327700-7">Density bounds for the sum of divisors function</a>, Math. Comp. 26 (1972), 773-777.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbundantNumber.html">Abundant Number</a>

%e For k=1 to 5, all numbers are deficients so a(k) = k in this range.

%e a(6) = 5 since 6 is the first number that is not deficient.

%t a[n_]:=Length[Select[Range[n],DivisorSigma[1,#]/#<2&]];a/@Range[68] (* _Ivan N. Ianakiev_, Apr 03 2015 *)

%o (PARI) a(n) = sum(k=1, n, sigma(k)/k < 2);

%o (MAGMA) [#[k:k in [1..n]| DivisorSigma(1,k) lt 2*k]:n in [1..70]]; // _Marius A. Burtea_, Nov 06 2019

%Y Cf. A000396 (perfect), A005100 (deficient), A005101 (abundant).

%Y Cf. A091194 (number of abundant numbers <= n).

%Y Cf. A256440.

%K nonn

%O 1,2

%A _Michel Marcus_, Apr 02 2015

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Last modified December 6 07:11 EST 2019. Contains 329785 sequences. (Running on oeis4.)