A392500 Numbers k > 1 whose largest proper divisor cannot be written as a sum of their other nontrivial divisors.

4, 6, 8, 9, 10, 14, 15, 16, 20, 21, 22, 25, 26, 27, 28, 32, 33, 34, 35, 38, 39, 44, 45, 46, 49, 50, 51, 52, 55, 57, 58, 62, 63, 64, 65, 68, 69, 70, 74, 75, 76, 77, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 104, 105, 106, 110, 111, 115, 116, 117, 118

Offset

1,1

Comments

Equivalently, k is a term if and only if it is composite (A002808) but not composable (A392440). We call these numbers 'noncomposable'.

This sequence = A392498 U A392499, thus, noncomposable numbers are either sparse (A392498) or rigid (A392499).

The set of nonnegative integers is the union {0, 1} U A000040 U A392440 U this sequence.

Semiprimes (A001358) are a subsequence.

Strict prime powers (A246547) are a subsequence.

Links

Table of n, a(n) for n=1..64.

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

Prog

(Python)  # Functions is_sparse and is_rigid are defined in A392498 and A392499.
def A392500_list(upto: int) -> list[int]:
    return [n for n in range(2, upto + 1) if bool(is_sparse(n)) or bool(is_rigid(n))]
print(A392500_list(118))

Crossrefs

Cf. A392440 (composable), A392498 (sparse), A392499 (rigid), A002808 (composite), A001358, A246547.

Sequence in context: A104211 A132858 A071941 * A188654 A330991 A180366

Adjacent sequences: A392497 A392498 A392499 * A392501 A392502 A392503

Keyword

nonn

Author

Peter Luschny, Jan 14 2026

Status

approved