OFFSET
1,4
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (c(i) + c(j) + c(k) + c(n-i-j-k)), where c(x) = [gcd(n,x) = 1] and [ ] is the Iverson bracket.
EXAMPLE
The partitions of 8 into 4 parts are: 1+1+1+5, 1+1+2+4, 1+1+3+3, 1+2+2+3, and 2+2+2+2. 8 is relatively prime to 1, 3, and 5. Since there are 12 total parts in these partitions that are coprime to 8, a(8) = 12.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 27 2023
STATUS
approved