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A235796 2*n - 1 - sigma(n). 9
0, 0, 1, 0, 3, -1, 5, 0, 4, 1, 9, -5, 11, 3, 5, 0, 15, -4, 17, -3, 9, 7, 21, -13, 18, 9, 13, -1, 27, -13, 29, 0, 17, 13, 21, -20, 35, 15, 21, -11, 39, -13, 41, 3, 11, 19, 45, -29, 40, 6, 29, 5, 51, -13, 37, -9, 33, 25, 57, -49, 59, 27, 21, 0, 45, -13, 65, 9, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Partial sums give A004125.

Also 0 together with A120444.

It appears that a(n) = 0 iff n is a power of 2.

Numbers n with a(n) = 0 are called "almost perfect", "least deficient" or "slightly defective" numbers.  See A000079. - Robert Israel, Jul 22 2014

a(n) = n - 2 iff n is prime.

a(n) = -1 iff n is a perfect number.

Also the alternating row sums of A239446. - Omar E. Pol, Jul 21 2014

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, New York, 2004.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A005408(n-1) - A000203(n).

a(n) = -1 - A033880(n). - Michel Marcus, Jan 27 2014

a(n) =  n - 1 - A001065(n). - Omar E. Pol, Jan 29 2014

a(n) = A033879(n) - 1. - Omar E. Pol, Jan 30 2014

a(n) = 2*n - 2 - A039653(n). - Omar E. Pol, Jan 31 2014

a(n) = (-1)*A237588(n). - Omar E. Pol, Feb 23 2014

a(n) = 2*n - A088580(n). - Omar E. Pol, Mar 23 2014

EXAMPLE

.     The positive     The sum of

n     odd numbers     divisors of n.      a(n)

1          1                1               0

2          3                3               0

3          5                4               1

4          7                7               0

5          9                6               3

6         11               12              -1

7         13                8               5

8         15               15               0

9         17               13               4

10        19               18               1

...

MATHEMATICA

Table[2n-1-DivisorSigma[1, n], {n, 70}] (* Harvey P. Dale, Jul 11 2014 *)

PROG

(PARI) vector(100, n, (2*n-1)-sigma(n)) \\ Colin Barker, Jan 27 2014

(MAGMA) [2*n-1-SumOfDivisors(n): n in [1..100]]; // Vincenzo Librandi, Feb 25 2014

CROSSREFS

Cf. A000079, A000203, A000396, A004125, A005408, A120444, A196020, A236104.

Sequence in context: A143467 A143315 A237588 * A120444 A094919 A328373

Adjacent sequences:  A235793 A235794 A235795 * A235797 A235798 A235799

KEYWORD

sign

AUTHOR

Omar E. Pol, Jan 25 2014

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)