Search: id:A005101
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%I A005101 M4825
%S A005101 12,18,20,24,30,36,40,42,48,54,56,60,66,70,72,78,80,84,88,90,96,100,102,
               104,
%T A005101 108,112,114,120,126,132,138,140,144,150,156,160,162,168,174,176,180,186,
               192,
%U A005101 196,198,200,204,208,210,216,220,222,224,228,234,240,246,252,258,260,264,
               270
%N A005101 Abundant numbers (sum of divisors of n exceeds 2n).
%C A005101 A number n is abundant if sigma(n) > 2n (this entry), perfect if sigma(n) 
               = 2n (cf. A000396), deficient if sigma(n) < 2n (cf. A005100), where 
               sigma(n) is the sum of the divisors of n (A000203).
%C A005101 It appears that for n>23, the result of (2*A001055)-A101113 is NOT 0 
               if n=A005101. [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Jun 
               01 2009]
%D A005101 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005101 L. E. Dickson, Theorems and tables on the sum of the divisors of a number, 
               Quart. J. Pure Appl. Math., 44 (1913), 264-296.
%D A005101 R. K. Guy, Unsolved Problems in Number Theory, B2.
%D A005101 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               59.
%H A005101 T. D. Noe, <a href="b005101.txt">Table of n, a(n) for n = 1..10000</a>
%H A005101 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">
               Abundancy : Some Resources </a>
%H A005101 J. Britton, <a href="http://britton.disted.camosun.bc.ca/perfect/jbperfect.htm">
               Perfect Number Analyser</a>
%H A005101 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php/AbundantNumber.html">abundant number</a>
%H A005101 M. Deleglise, <a href="http://projecteuclid.org/Dienst/UI/1.0/Summarize/
               euclid.em/1048515661">Bounds for the density of abundant integers</
               a>
%H A005101 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AbundantNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A005101 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Abundance.html">Abundance</a>
%H A005101 Wikipedia, <a href="http://www.fact-index.com/a/ab/abundant_number.html">
               Abundant number</a>
%H A005101 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A005101 a(n) is asymptotic to C*n with C=4.038.. (Deleglise 1998) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Sep 04 2002
%F A005101 If n is a member so is every positive multiple of n. "Primitive" members 
               are in A091191.
%p A005101 with(numtheory): for n from 1 to 270 do if sigma(n)>2*n then printf(`%d,
               `,n) fi: od:
%t A005101 abQ[n_] := DivisorSigma[1, n] > 2n; Select[ Range[270], abQ[ # ] &] (from 
               Robert G. Wilson v (rgwv(at)rgwv.com), Sep 15 2005)
%o A005101 (PARI) isA005101(n) = (sigma(n) > 2*n) [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Nov 07 2009]
%Y A005101 Cf. A005835, A005100, A091194, A091196, A080224, A091191 (primitive).
%Y A005101 Cf. A005231 and A006038 (odd abundant numbers).
%Y A005101 Cf. A094268 (n consecutive abundant numbers).
%Y A005101 Sequence in context: A126706 A123711 A059404 this_sequence A124626 A087245 
               A153501
%Y A005101 Adjacent sequences: A005098 A005099 A005100 this_sequence A005102 A005103 
               A005104
%K A005101 nonn,easy,core,nice
%O A005101 1,1
%A A005101 N. J. A. Sloane (njas(AT)research.att.com).
%E A005101 More terms from David W. Wilson (davidwwilson(AT)comcast.net).

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