A343100 Number of partitions of n into 3 parts, at least 2 of which are coprime.

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

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