This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A256562 Number of deficient numbers <= n. 1


%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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