Search: id:A005100
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%I A005100 M0514
%S A005100 1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29,31,32,33,
%T A005100 34,35,37,38,39,41,43,44,45,46,47,49,50,51,52,53,55,57,58,59,61,62,63,
%U A005100 64,65,67,68,69,71,73,74,75,76,77,79,81,82,83,85,86
%N A005100 Deficient numbers: numbers n such that sigma(n) < 2n.
%C A005100 A number n is abundant if sigma(n) > 2n (cf. A005101), perfect if sigma(n) 
               = 2n (cf. A000396), deficient if sigma(n) < 2n (this entry), where 
               sigma(n) is the sum of the divisors of n (A000203).
%C A005100 Also, numbers n such that A033630(n) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 02 2007
%D A005100 R. K. Guy, Unsolved Problems in Number Theory, B2.
%D A005100 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005100 T. D. Noe, <a href="b005100.txt">Table of n, a(n) for n = 1..10000</a>
%H A005100 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">
               Abundancy : Some Resources </a>
%H A005100 J. Britton, <a href="http://britton.disted.camosun.bc.ca/perfect/jbperfect.htm">
               Perfect Number Analyser</a>
%H A005100 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DeficientNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A005100 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Abundance.html">Abundance</a>
%H A005100 Wikipedia, <a href="http://en.wikipedia.org/wiki/Deficient_number">Deficient 
               number</a>
%H A005100 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%p A005100 with(numtheory); s := proc(n) local i,j,ans; ans := [ ]; j := 0; for 
               i while j<n do if sigma(i)<2*i then ans := [ op(ans),i ]; j := j+1; 
               fi; od; RETURN(ans); end; # s(k) returns terms of sequence through 
               k
%t A005100 Select[Range[100], DivisorSigma[1, # ] < 2*# &] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Mar 31 2006
%o A005100 (PARI) isA005100(n) = (sigma(n) < 2*n) [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Nov 08 2009]
%Y A005100 Cf. A005101.
%Y A005100 By definition, the weird numbers A006037 are not in this sequence.
%Y A005100 Sequence in context: A088725 A094520 A136447 this_sequence A051772 A049093 
               A098901
%Y A005100 Adjacent sequences: A005097 A005098 A005099 this_sequence A005101 A005102 
               A005103
%K A005100 nonn,easy,core,nice,new
%O A005100 1,2
%A A005100 N. J. A. Sloane (njas(AT)research.att.com).
%E A005100 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Mar 31 2006

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