A340284 Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to each of the other two parts.

0, 0, 1, 1, 1, 2, 1, 3, 3, 4, 2, 7, 4, 9, 7, 9, 7, 15, 9, 18, 14, 19, 12, 27, 15, 26, 21, 30, 21, 44, 25, 43, 35, 46, 34, 58, 34, 59, 46, 64, 43, 82, 47, 80, 64, 83, 58, 107, 65, 106, 79, 110, 75, 137, 86, 128, 98, 132, 92, 172, 96, 155, 122, 161, 118, 198, 119, 188, 147

Offset

1,6

Links

Table of n, a(n) for n=1..69.

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(i,k)) * floor(1/gcd(i,n-i-k)).

Mathematica

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

Crossrefs

Cf. A340283, A340285.

Sequence in context: A363625 A057938 A144623 * A218975 A048619 A116087

Adjacent sequences: A340281 A340282 A340283 * A340285 A340286 A340287

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved