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Number of ordered factorizations of n into factors > 4.
4

%I #5 Mar 23 2024 20:29:39

%S 1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,1,1,1,1,

%T 3,2,1,1,1,3,1,3,1,1,3,1,1,3,2,3,1,1,1,3,3,3,1,1,1,5,1,1,3,2,3,3,1,1,

%U 1,5,1,5,1,1,3,1,3,3,1,5,2,1,1,5,3,1,1,3,1,7,3,1

%N Number of ordered factorizations of n into factors > 4.

%F a(1) = 1; a(n) = Sum_{d|n, n/d > 4} a(d).

%e a(30) = 3: 30 = 5*6 = 6*5.

%t a[n_] := a[n] = If[n == 1, n, Sum[If[n/d > 4, a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 92}]

%Y Cf. A002033, A017899, A074206, A185325, A371209, A371211, A371213.

%K nonn

%O 1,25

%A _Ilya Gutkovskiy_, Mar 15 2024