A392438 2-composable numbers: even numbers k for which k/2 is a sum of the other nontrivial divisors of k.

12, 18, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 90, 96, 100, 102, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260

Offset

1,1

Comments

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.

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.

Links

Table of n, a(n) for n=1..56.

Peter Luschny, Composable, rigid, and sparse numbers. A Python notebook.

Example

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

Prog

(Python) # Function 'is_composable' is defined in A392440 (see also links).
def A392438_list(upto: int) -> list[int]:
    return [n for n in range(4, upto+1, 2) if 2 == is_composable(n)]

Crossrefs

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

Sequence in context: A175837 A392440 A136446 * A074726 A341475 A091013

Adjacent sequences: A392435 A392436 A392437 * A392439 A392440 A392441

Keyword

nonn

Author

Peter Luschny, Jan 12 2026

Status

approved