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A303051
Number of partitions of n into two distinct parts (p,q) such that p, q and p+q are all squarefree.
1
0, 0, 1, 0, 1, 1, 2, 0, 0, 1, 2, 0, 3, 2, 3, 0, 4, 0, 3, 0, 4, 4, 4, 0, 0, 4, 0, 0, 5, 4, 5, 0, 6, 6, 6, 0, 7, 6, 7, 0, 8, 7, 9, 0, 0, 7, 8, 0, 0, 0, 7, 0, 10, 0, 7, 0, 10, 10, 9, 0, 11, 10, 0, 0, 11, 10, 11, 0, 12, 12, 11, 0, 13, 13, 0, 0, 14, 12, 14, 0, 0
OFFSET
1,7
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} mu(n)^2 * mu(i)^2 * mu(n-i)^2, where mu is the Möbius function (A008683).
MATHEMATICA
Table[Sum[MoebiusMu[n]^2 MoebiusMu[i]^2 MoebiusMu[n - i]^2, {i, Floor[(n - 1)/2]}], {n, 100}]
PROG
(PARI) a(n) = sum(i=1, (n-1)\2, moebius(n)^2*moebius(i)^2*moebius(n-i)^2); \\ Michel Marcus, Apr 17 2018
CROSSREFS
Sequence in context: A357237 A277808 A105964 * A324044 A364046 A001899
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 17 2018
STATUS
approved