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!)
A234307 a(n) = Sum_{i=1..n} gcd(2*n-i, i). 3
1, 3, 6, 8, 11, 17, 16, 20, 27, 31, 26, 44, 31, 45, 60, 48, 41, 75, 46, 80, 87, 73, 56, 108, 85, 87, 108, 116, 71, 165, 76, 112, 141, 115, 158, 192, 91, 129, 168, 196, 101, 239, 106, 188, 261, 157, 116, 256, 175, 235, 222, 224, 131, 297, 256, 284, 249, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum of the GCD's of the smallest and largest parts in the partitions of 2n into exactly two parts.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..n} gcd(2*n-i, i).

EXAMPLE

a(6) = 17; the partitions of 2(6) = 12 into two parts are: (11,1),(10,2),(9,3),(8,4),(7,5),(6,6). Then a(6) = gcd(11,1) + gcd(10,2) + gcd(9,3) + gcd(8,4) + gcd(7,5) + gcd(6,6). = 1 + 2 + 3 + 4 + 1 + 6 = 17.

MAPLE

A234307:=n->add( gcd(2*n-i, i), i=1..n); seq(A234307(n), n=1..100);

MATHEMATICA

Table[Sum[GCD[2n - i, i], {i, n}], {n, 100}]

PROG

(PARI) a(n) = sum(i=1, n, gcd(i, 2*n-i)); \\ Michel Marcus, Dec 23 2013

CROSSREFS

Cf. A001105 (Sum of Parts), A002378 (Differences of Parts).

Sequence in context: A190430 A188018 A289241 * A175769 A160277 A233541

Adjacent sequences:  A234304 A234305 A234306 * A234308 A234309 A234310

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 22 2013

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 July 4 18:38 EDT 2020. Contains 335448 sequences. (Running on oeis4.)