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Search: id:A005100
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| A005100 |
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Deficient numbers: numbers n such that sigma(n) < 2n.
(Formerly M0514)
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+0
55
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| 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, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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).
Also, numbers n such that A033630(n) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 02 2007
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B2.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
Walter Nissen, Abundancy : Some Resources
J. Britton, Perfect Number Analyser
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Abundance
Wikipedia, Deficient number
Index entries for "core" sequences
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MAPLE
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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
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MATHEMATICA
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Select[Range[100], DivisorSigma[1, # ] < 2*# &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 31 2006
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PROGRAM
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(PARI) isA005100(n) = (sigma(n) < 2*n) [From Michael Porter (michael_b_porter(AT)yahoo.com), Nov 08 2009]
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CROSSREFS
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Cf. A005101.
By definition, the weird numbers A006037 are not in this sequence.
Sequence in context: A088725 A094520 A136447 this_sequence A051772 A049093 A098901
Adjacent sequences: A005097 A005098 A005099 this_sequence A005101 A005102 A005103
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KEYWORD
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nonn,easy,core,nice,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 31 2006
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