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Number of compositions of n into two non-refactorable parts.
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%I #3 Jan 07 2024 00:37:02

%S 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,

%T 17,16,19,20,19,20,24,22,23,22,23,24,27,24,27,28,27,28,34,32,31,32,35,

%U 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

%N Number of compositions of n into two non-refactorable parts.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

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

%e 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.

%t 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}]

%Y Cf. A159973, A368625.

%K nonn,easy

%O 1,7

%A _Wesley Ivan Hurt_, Jan 07 2024