login
A335230
Number of partitions of n into 3 refactorable parts.
1
0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 2, 3, 3, 4, 2, 1, 1, 2, 2, 3, 2, 2, 2, 4, 2, 2, 1, 3, 2, 4, 3, 2, 1, 2, 3, 5, 2, 1, 2, 4, 1, 4, 3, 2, 2, 6, 2, 3, 2, 2, 2, 6, 2, 1, 3, 4, 1, 5, 4, 4, 2, 6, 3, 3, 1, 4, 5, 7, 3, 5, 3, 5, 2, 6, 4, 6, 3, 7
OFFSET
0,12
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} chi(i/d(i)) * chi(j/d(j)) * chi((n-i-j)/d(n-i-j)), where chi(n) = 1 - ceiling(n) + floor(n) and d is the number of divisors of n (A000005).
EXAMPLE
a(6) = 1; There is one partition of 6 into 3 refactorable parts, (2,2,2).
a(11) = 2; There are two partitions of 11 into 3 refactorable parts, (9,1,1) and (8,2,1).
CROSSREFS
Cf. A000005 (tau), A033950 (refactorable numbers), A335231.
Sequence in context: A164562 A058188 A333851 * A300752 A300751 A070000
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jun 09 2020
STATUS
approved