A340280 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A340280

Number of partitions of n into 3 parts such that the 'middle' 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, 22, 18, 28, 24, 32, 30, 42, 32, 48, 42, 52, 48, 64, 48, 74, 64, 78, 72, 90, 72, 104, 88, 108, 96, 126, 96, 140, 118, 142, 130, 166, 128, 180, 150, 186, 164, 212, 162, 222, 190, 230, 206, 260, 192, 280, 236, 280, 252

(list; graph; refs; listen; history; text; internal format)

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

MATHEMATICA

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

CROSSREFS

Cf. A340279, A340282.