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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235799 a(n) = n^2 - sigma(n). 4
0, 1, 5, 9, 19, 24, 41, 49, 68, 82, 109, 116, 155, 172, 201, 225, 271, 285, 341, 358, 409, 448, 505, 516, 594, 634, 689, 728, 811, 828, 929, 961, 1041, 1102, 1177, 1205, 1331, 1384, 1465, 1510, 1639, 1668, 1805, 1852, 1947, 2044, 2161, 2180, 2344, 2407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A000290(n) - A000203(n).

a(n) = A024916(n-1) + A004125(n), n > 1.

G.f.: x*(1 + x)/(1 - x)^3 - Sum_{k>=1} x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Mar 17 2017

EXAMPLE

1) Illustration of initial terms:

---------------------------------------------------------

n    1    2      3        4          5            6

---------------------------------------------------------

.        _     _ _     _ _ _     _ _ _ _     _ _ _ _ _

.    .  |_|.  |_| |.  |_| | |.  |_| | | |.  |_| | | | |.

.        . .  |_|_|.  |_|_| |.  |_|_| | |.  |_|_| | | |.

.              . O .  |_|.|_|.  |_| |_| |.  |_| |_| | |.

.                      . . O .  |_|_|O|_|.  |_|_|.|_| |.

.                                . O O O .  |_|. . O|_|.

.                                            . . . O O .

.

---------------------------------------------------------

a(n): 0   1      5        9         19           24

---------------------------------------------------------

b(n): 1   3      4        7          6           12

c(n): 1   4      9       16         25           36

---------------------------------------------------------

d(n): 0   1      4        8         15           21

e(n): 0   0      1        1          4            3

---------------------------------------------------------

Where:

a(n) equals the total number of square cells and circles in the diagram.

b(n) = A000203(n), equals the number of dots.

c(n) = A000290(n), equals the matrix n X n.

d(n) = A024916(n-1), equals the number of square cells.

e(n) = A004125(n), equals the number of circles.

.

---------------------------------------------------------

2) Illustration of initial terms using a symmetric diagram which arises from the structure of A236104:

---------------------------------------------------------

n    1    2      3        4          5            6

---------------------------------------------------------

.        _     _ _     _ _ _     _ _ _ _     _ _ _ _ _

.    .  |_|.  |_| |.  |_| | |.  |_| | | |.  |_| | | | |.

.        . .  |_ _|.  |_ _|_|.  |_ _|_| |.  |_ _|_| | |.

.              . . O  |_ _|. .  |_ _|  _|.  |_ _|  _|_|.

.                      . . . O  |_ _ _|O O  |_ _ _|. . .

.                                . . . O O  |_ _ _|. . O

.                                            . . . . O O

---------------------------------------------------------

a(n): 0   1      5        9         19           24

---------------------------------------------------------

MATHEMATICA

Table[n^2-DivisorSigma[1, n], {n, 50}] (* Harvey P. Dale, Sep 02 2016 *)

PROG

(PARI) vector(50, n, n^2 - sigma(n)) \\ G. C. Greubel, Oct 31 2018

(MAGMA) [n^2 - DivisorSigma(1, n): n in [1..50]]; // G. C. Greubel, Oct 31 2018

CROSSREFS

Cf. A000203, A000290, A004125, A024916, A120444, A196020, A236104, A236112, A237593.

Sequence in context: A160722 A255652 A061202 * A295966 A060161 A282730

Adjacent sequences:  A235796 A235797 A235798 * A235800 A235801 A235802

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 24 2014

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 14:43 EST 2019. Contains 329126 sequences. (Running on oeis4.)