login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033879 Deficiency of n, or 2n - (sum of divisors of n). 44
1, 1, 2, 1, 4, 0, 6, 1, 5, 2, 10, -4, 12, 4, 6, 1, 16, -3, 18, -2, 10, 8, 22, -12, 19, 10, 14, 0, 28, -12, 30, 1, 18, 14, 22, -19, 36, 16, 22, -10, 40, -12, 42, 4, 12, 20, 46, -28, 41, 7, 30, 6, 52, -12, 38, -8, 34, 26, 58, -48, 60, 28, 22, 1, 46, -12, 66, 10, 42, -4, 70, -51 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Records for the sequence of the absolute values are in A075728 and the indices of these records in A074918. - R. J. Mathar, Mar 02 2007

a(n) = 1 iff n is a power of 2. a(n) = n - 1 iff n is prime. - Omar E. Pol, Jan 30 2014

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, Section B2.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..2000

Nichole Davis, Dominic Klyve and Nicole Kraght, On the difference between an integer and the sum of its proper divisors, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493

Jose A. B. Dris, Conditions Equivalent to the Descartes-Frenicle-Sorli Conjecture on Odd Perfect Numbers, arXiv preprint arXiv:1610.01868 [math.NT], 2016.

Jose Arnaldo B. Dris, Analysis of the Ratio D(n)/n, arXiv:1703.09077 [math.NT], 2017.

Index entries for sequences related to sigma(n)

FORMULA

a(n) = -A033880(n).

a(n) = A005843(n) - A000203(n). - Omar E. Pol, Dec 14 2008

a(n) = n - A001065(n). - Omar E. Pol, Dec 27 2013

G.f.: 2*x/(1 - x)^2 - Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Jan 24 2017

a(n) = A286385(n) - A252748(n). - Antti Karttunen, May 13 2017

EXAMPLE

For n = 10 the divisors of 10 are 1, 2, 5, 10, so the deficiency of 10 is 10 minus the sum of its proper divisors or simply 10 - 5 - 2 - 1 = 2. - Omar E. Pol, Dec 27 2013

MAPLE

with(numtheory): A033879:=n->2*n-sigma(n): seq(A033879(n), n=1..100);

MATHEMATICA

Table[2n-DivisorSigma[1, n], {n, 80}] (* Harvey P. Dale, Oct 24 2011 *)

PROG

(PARI) a(n)=2*n-sigma(n) \\ Charles R Greathouse IV, Oct 13 2016

CROSSREFS

Cf. A000203, A005101, A033880, A074918, A075728, A192895, A286385, A286449.

Sequence in context: A103977 A109883 A033880 * A033883 A106316 A126707

Adjacent sequences:  A033876 A033877 A033878 * A033880 A033881 A033882

KEYWORD

sign,nice,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

Definition corrected Jul 04 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified October 17 05:32 EDT 2017. Contains 293467 sequences.