A368821 Number of compositions of n into 2 refactorable parts.

0, 1, 2, 1, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 1, 2, 1, 2, 4, 2, 0, 0, 1, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, 0, 3, 2, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, 5, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 4, 2, 0, 0, 3, 2, 4, 0, 2, 0, 2, 0, 5, 4, 2, 0, 4, 2, 2, 0, 2, 4, 4, 0, 6, 2, 0, 0, 10, 4

Offset: 1

Author

Wesley Ivan Hurt, Jan 06 2024

Keywords

• nonn
• easy

Examples

			a(10) = 4. There are 4 ordered ways to write 10 as the sum of two refactorable numbers: 1 + 9 = 2 + 8 = 8 + 2 = 9 + 1.
a(36) = 3. There are 3 ordered ways to write 36 as the sum of two refactorable numbers: 12 + 24 = 18 + 18 = 24 + 12.
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A033950, A336040.

Programs

Mathematica

Table[Sum[(1 - Ceiling[k/DivisorSigma[0, k]] + Floor[k/DivisorSigma[0, k]]) (1 - Ceiling[(n - k)/DivisorSigma[0, (n - k)]] + Floor[(n - k)/DivisorSigma[0, (n - k)]]), {k, n - 1}], {n, 100}]

Formula

a(n) = Sum_{k=1..n-1} c(k) * c(n-k), where c = A336040.