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!)
A343100 Number of partitions of n into 3 parts, at least 2 of which are coprime. 0
0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 10, 8, 14, 12, 16, 16, 24, 18, 30, 24, 32, 30, 44, 32, 50, 42, 54, 48, 70, 48, 79, 64, 80, 72, 96, 72, 113, 90, 112, 96, 138, 96, 153, 120, 144, 132, 182, 128, 195, 150, 192, 168, 232, 162, 239, 192, 240, 210, 287, 192, 305, 240, 288, 256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..64.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(floor(1/gcd(i, j)) + floor(1/gcd(i, n-i-j)) + floor(1/gcd(j, n-i-j))).

EXAMPLE

a(12) = 8; [10,1,1], [9,2,1], [8,3,1], [7,4,1], [7,3,2], [6,5,1], [5,5,2], [5,4,3].

MATHEMATICA

Table[Sum[Sum[Sign[Floor[1/GCD[i, j]] + Floor[1/GCD[i, n - i - j]] + Floor[1/GCD[j, n - i - j]]], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]

CROSSREFS

Cf. A023023, A069905.

Sequence in context: A029009 A340280 A340279 * A023023 A184157 A008643

Adjacent sequences:  A343097 A343098 A343099 * A343101 A343102 A343103

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Apr 05 2021

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 June 14 19:28 EDT 2021. Contains 345038 sequences. (Running on oeis4.)