A368822 Number of compositions of n into two non-refactorable parts.

0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 4, 3, 4, 5, 4, 6, 8, 8, 8, 11, 10, 9, 10, 12, 12, 15, 14, 13, 14, 17, 16, 19, 20, 19, 20, 24, 22, 23, 22, 23, 24, 27, 24, 27, 28, 27, 28, 34, 32, 31, 32, 35, 34, 37, 36, 37, 38, 41, 38, 41, 40, 41, 40, 45, 44, 43, 44, 49, 48, 47, 48, 52, 50, 53, 50, 53, 52

Offset

1,7

Links

Table of n, a(n) for n=1..77.

Index entries for sequences related to compositions

Formula

a(n) = Sum_{k=1..n-1} c(k) * c(n-k), where c = A368625.

Example

a(12) = 3 since there are 3 ordered ways to write 12 as the sum of two non-refactorable numbers: 5 + 7 = 6 + 6 = 7 + 5.

Mathematica

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

Crossrefs

Cf. A159973, A368625.

Sequence in context: A017870 A017860 A328765 * A270434 A204982 A017850

Adjacent sequences: A368819 A368820 A368821 * A368823 A368824 A368825

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 07 2024

Status

approved