A340285 Number of partitions of n into 3 parts such that the largest part is relatively prime to each of the other two parts.

0, 0, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 6, 9, 8, 11, 10, 16, 12, 18, 15, 20, 19, 28, 21, 30, 25, 34, 27, 44, 30, 44, 36, 50, 39, 60, 43, 62, 51, 69, 52, 85, 56, 83, 68, 86, 68, 109, 71, 109, 84, 110, 84, 138, 91, 132, 105, 138, 104, 176, 111, 162, 131, 171, 127, 204, 129, 193

Offset

1,6

Links

Table of n, a(n) for n=1..68.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} floor(1/gcd(n-i-k,k)) * floor(1/gcd(n-i-k,i)).

Mathematica

Table[Sum[Sum[Floor[1/GCD[n - i - k, k]]*Floor[1/GCD[n - i - k, i]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]

Crossrefs

Cf. A340283, A340284.

Sequence in context: A304430 A086609 A341140 * A341462 A035031 A035032

Adjacent sequences: A340282 A340283 A340284 * A340286 A340287 A340288

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved