A392438 - OEIS

%I #28 Feb 04 2026 22:29:19

%S 12,18,24,30,36,40,42,48,54,56,60,66,72,78,80,84,90,96,100,102,108,

%T 112,114,120,126,132,138,140,144,150,156,160,162,168,174,176,180,186,

%U 192,196,198,200,204,208,210,216,220,222,224,228,234,240,246,252,258,260

%N 2-composable numbers: even numbers k for which k/2 is a sum of the other nontrivial divisors of k.

%C An integer n > 1 is a term if and only if n is even, and its largest proper divisor L = n/2 can be represented as the sum of some subset of its other nontrivial divisors. A 'nontrivial divisor' d of n is any divisor that is 1 < d < n. Let D_{2}(n) = {1 < d < L : d | n}. Then n is a term if there exists a subset S of D_{2}(n) such that L = Sum(S). Written in this form, n is recognizable as a p-composable number with p = 2, where the case for general p is defined in A392440.

%C Differs first from A136446 at n = 220, where the first odd semiperfect number 945 (resp. the first odd abundant number) appears in A136446, see A005231.

%H Peter Luschny, <a href="https://github.com/PeterLuschny/Gists/blob/main/ComposableRigidSparse.ipynb">Composable, rigid, and sparse numbers</a>. A Python notebook.

%e 12 is 2-composable as it can be written as the sum of a subset of its nontrivial divisors, namely as 2 + 4 + 6, and {2, 4} is a subset drawn from divisors strictly smaller than 6.

%e 6 is not 2-composable although it is semiperfect (1 + 2 + 3 = 6).

%o (Python) # Function 'is_composable' is defined in A392440 (see also links).

%o def A392438_list(upto: int) -> list[int]:

%o     return [n for n in range(4, upto+1, 2) if 2 == is_composable(n)]

%Y Cf. A392440, A392437 (p=3), A392439, A392500, A000040, A005231, A005835, A070824, A136446.

%K nonn

%O 1,1

%A _Peter Luschny_, Jan 12 2026