A340286 Number of partitions of n into 3 parts such that at least two parts share a common factor > 1.

0, 0, 0, 0, 1, 1, 3, 2, 5, 4, 8, 5, 12, 8, 15, 13, 20, 12, 26, 17, 30, 25, 37, 22, 45, 33, 50, 39, 60, 32, 71, 50, 75, 58, 86, 54, 100, 71, 104, 79, 122, 68, 136, 95, 138, 112, 159, 92, 175, 119, 181, 140, 203, 116, 217, 157, 225, 176, 251, 133, 274, 195, 273, 212, 300

Offset: 1

Author

Wesley Ivan Hurt, Jan 03 2021

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A307719.

Programs

Mathematica

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

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1 - [gcd(k,i) * gcd(k,n-i-k) * gcd(i,n-i-k) = 1]), where [ ] is the Iverson bracket.