OFFSET
1,12
FORMULA
a(n) = Sum_{k=1..floor(n/2)} (1 - floor(1/gcd(k,n-k))) * c(k) * c(n-k), where c(n) is the characteristic function of composite numbers.
EXAMPLE
a(12) = 2; (8,4) and (6,6).
a(15) = 1; (9,6).
a(16) = 3; (12,4), (10,6), and (8,8).
a(18) = 4; (14,4), (12,6), (10,8), and (9,9).
MATHEMATICA
Table[Sum[(1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - k] + PrimePi[n - k - 1]) (1 - Floor[1/GCD[k, n - k]]), {k, Floor[n/2]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 06 2021
STATUS
approved