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A368821
Number of compositions of n into 2 refactorable parts.
0
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
1,3
FORMULA
a(n) = Sum_{k=1..n-1} c(k) * c(n-k), where c = A336040.
EXAMPLE
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.
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}]
CROSSREFS
Sequence in context: A123863 A244560 A331812 * A250002 A035195 A073797
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 06 2024
STATUS
approved