A335230 Number of partitions of n into 3 refactorable parts.

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

Links

Table of n, a(n) for n=0..92.

Index entries for sequences related to partitions

Eric Weisstein's World of Mathematics, Refactorable Number

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

Adjacent sequences: A335227 A335228 A335229 * A335231 A335232 A335233

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 09 2020

Status

approved