

A033879


Deficiency of n, or 2n  (sum of divisors of n).


43



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
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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, 493504; DOI: 10.2140/involve.2013.6.493
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*nsigma(n): seq(A033879(n), n=1..100);


MATHEMATICA

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


PROG

(PARI) a(n)=2*nsigma(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


AUTHOR

N. J. A. Sloane


EXTENSIONS

Definition corrected Jul 04 2005


STATUS

approved



