OFFSET
1,3
FORMULA
a(n) = Sum_{k=1..floor(n/2)} k * (n-k) * mu(k*(n-k))^2, where mu is the Möbius function (A008683).
EXAMPLE
a(13) = 94; The partitions of 13 into two positive integer parts (s,t) where s <= t are (1,12), (2,11), (3,10), (4,9), (5,8), (6,7). The corresponding products are 1*12, 2*11, 3*10, 4*9, 5*8, and 6*7. The sum of the squarefree products from this list is 22 + 30 + 42 = 94.
MATHEMATICA
Table[Sum[k (n - k) MoebiusMu[k (n - k)]^2, {k, Floor[n/2]}], {n, 80}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 08 2021
STATUS
approved