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A005100 Deficient numbers: numbers n such that sigma(n) < 2n.
(Formerly M0514)
101
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; refs; listen; history; text; internal format)
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

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Last modified August 29 14:12 EDT 2014. Contains 246192 sequences.