

A005100


Deficient numbers: numbers n such that sigma(n) < 2n.
(Formerly M0514)


103



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
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OFFSET

1,2


COMMENTS

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, Mar 02 2007


REFERENCES

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).


LINKS

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, Deficient Number
Eric Weisstein's World of Mathematics, Abundance
Wikipedia, Deficient number
Index entries for "core" sequences


MAPLE

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


MATHEMATICA

Select[Range[100], DivisorSigma[1, # ] < 2*# &]  Stefan Steinerberger, Mar 31 2006


PROG

(PARI) isA005100(n) = (sigma(n) < 2*n) [From Michael B. Porter, Nov 08 2009]


CROSSREFS

Cf. A005101.
By definition, the weird numbers A006037 are not in this sequence.
Sequence in context: A088725 A094520 A136447 * A051772 A049093 A098901
Adjacent sequences: A005097 A005098 A005099 * A005101 A005102 A005103


KEYWORD

nonn,easy,core,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Stefan Steinerberger, Mar 31 2006


STATUS

approved



