login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006580 a(n) = Sum_{k=1..n-1} lcm(k,n-k).
(Formerly M3336)
5
0, 0, 1, 4, 8, 20, 21, 56, 60, 96, 105, 220, 152, 364, 301, 360, 464, 816, 549, 1140, 760, 1036, 1221, 2024, 1196, 2200, 2041, 2484, 2184, 4060, 2205, 4960, 3664, 4224, 4641, 5180, 4008, 8436, 6517, 7072, 5980, 11480, 6321, 13244, 8888, 9540, 11661, 17296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

Marc LeBrun, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1000 terms from Reinhard Zumkeller)

M. Le Brun, Email to N. J. A. Sloane, Jul 1991

FORMULA

For n > 0, a(n) = (n/6)*Sum_{d|n} (d*phi(d) - A023900(d)). - Sebastian Karlsson, Oct 02 2021

MAPLE

a:= n-> add(ilcm(j, n-j), j=0..n):

seq(a(n), n=0..70);  # Alois P. Heinz, Aug 25 2019

MATHEMATICA

Table[ Sum[ LCM[ k, n-k ], {k, 1, n-1} ], {n, 2, 50} ] (* Olivier Gérard, Aug 15 1997 *)

PROG

(Haskell)

a006580 n = a006580_list !! (n-1)

a006580_list = map sum a003990_tabl

-- Reinhard Zumkeller, Aug 05 2012

(PARI) a(n) = sum(k=1, n-1, lcm(k, n-k)); \\ Michel Marcus, Aug 11 2017

CROSSREFS

Antidiagonal sums of array A003990.

Cf. A209295.

Cf. A000010, A023900.

Sequence in context: A273143 A273174 A178447 * A061814 A087254 A160726

Adjacent sequences:  A006577 A006578 A006579 * A006581 A006582 A006583

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Olivier Gérard, Aug 15 1997

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 2 18:53 EDT 2022. Contains 357228 sequences. (Running on oeis4.)