A340278 Number of partitions of n into 3 parts whose smallest and largest parts are relatively prime.

0, 0, 1, 1, 2, 2, 4, 4, 5, 6, 9, 8, 11, 11, 13, 15, 19, 18, 23, 22, 24, 26, 32, 31, 37, 38, 42, 43, 50, 47, 55, 55, 59, 62, 68, 68, 78, 78, 83, 85, 96, 93, 105, 104, 108, 112, 124, 121, 132, 131, 138, 141, 154, 151, 162, 164, 172, 176, 191, 187, 205, 205, 212, 217, 228, 226

Offset

1,5

Links

Table of n, a(n) for n=1..66.

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(k,n-i-k)).

Mathematica

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

Crossrefs

Cf. A023023, A340275, A340276.

Sequence in context: A219029 A090168 A342498 * A337765 A266690 A230421

Adjacent sequences: A340275 A340276 A340277 * A340279 A340280 A340281

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved