login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162907 Sum of all numbers from tau(n) to sigma(n). 1
1, 5, 9, 25, 20, 72, 35, 114, 88, 165, 77, 391, 104, 294, 294, 486, 170, 765, 209, 888, 522, 660, 299, 1802, 493, 897, 814, 1581, 464, 2600, 527, 2001, 1170, 1479, 1170, 4150, 740, 1824, 1590, 4067, 902, 4628, 989, 3555, 3066, 2622, 1175, 7705, 1650, 4356, 2622, 4836 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000005(n) + (A000005(n)+1) + ... + A000203(n) = A000217(A000203(n)) - A000217(A000005(n)-1).

EXAMPLE

From Antti Karttunen, Sep 10 2017: (Start)

For n=1, tau(1) = sigma(1) = 1, thus a(1) = 1.

For n=2, tau(2) = 2 & sigma(2) = 3, thus a(2) = 2 + 3 = 5

For n=3, tau(3) = 2 & sigma(3) = 4, thus a(3) = 2 + 3 + 4 = 9.

For n=4, tau(4) = 3 & sigma(4) = 7, thus a(4) = 3 + 4 + 5 + 6 + 7 = 25. (End)

MAPLE

A000217 := proc(n) n*(n+1) /2; end: A162907 := proc(n) A000217(numtheory[sigma](n)) - A000217(numtheory[tau](n)-1) ; end: seq(A162907(n), n=1..100) ; # R. J. Mathar, Jul 21 2009

# second Maple program:

with(numtheory):

a:= n-> ((u, o)-> (u+o)*(o-u+1)/2)(tau(n), sigma(n)):

seq(a(n), n=1..80);  # Alois P. Heinz, Sep 10 2017

PROG

(PARI)

A000217(n) = n * (n + 1) / 2;

A162907(n) = (A000217(sigma(n)) - A000217(numdiv(n)-1)); \\ Antti Karttunen, Sep 10 2017, after the Maple-code.

CROSSREFS

Cf. A000005, A000203, A000217.

Sequence in context: A272256 A132354 A146419 * A165345 A177240 A074741

Adjacent sequences:  A162904 A162905 A162906 * A162908 A162909 A162910

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Jul 17 2009

EXTENSIONS

Approximately half of the entries corrected by R. J. Mathar, Jul 21 2009

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 February 26 03:24 EST 2020. Contains 332272 sequences. (Running on oeis4.)