A340279 Number of partitions of n into 3 parts such that the smallest part is relatively prime to at least one other part.

0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 10, 8, 14, 12, 16, 16, 24, 18, 30, 24, 32, 30, 43, 32, 49, 42, 54, 48, 68, 48, 78, 64, 80, 72, 93, 72, 110, 90, 111, 96, 134, 96, 148, 120, 144, 132, 175, 128, 187, 150, 189, 168, 221, 162, 230, 191, 236, 209, 273, 192, 293, 239, 285, 255

Offset

1,5

Links

Table of n, a(n) for n=1..64.

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Crossrefs

Cf. A340278, A340280.

Sequence in context: A328422 A029009 A340280 * A343100 A023023 A184157

Adjacent sequences: A340276 A340277 A340278 * A340280 A340281 A340282

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 02 2021

Status

approved