A392333 Non-semiprime composite numbers e such that there is no 0<a<b<c<d<e for which a! * b! * c! * d! * e! is a perfect square.

16523, 20387, 20683, 21229, 21793, 21827, 22591, 22997, 24769, 25051, 25789, 26129, 27347, 27521, 28379, 28613, 29003, 29341, 29419, 29563, 29783, 30073, 30659, 31093, 31447, 32227, 32383, 32513, 32591, 32759, 32981, 33031, 33337, 33449, 33497, 35351, 35711

Offset

1,1

Comments

Terms in A389148 that are not semiprimes. Subsequence of A350352.

a(1)-a(657) are all sphenic numbers. What is the first term that has 4 or more prime factors?

Links

Chai Wah Wu, Table of n, a(n) for n = 1..657

Thomas Bloom, Problem 374, Erdős Problems.

P. Erdős and R. L. Graham, On products of factorials, Bull. Inst. Math. Acad. Sinica 4 (1976), pp. 337-355.

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique (1980).

Crossrefs

Cf. A001358, A388851, A387184, A389148, A005117, A350352, A007304.

Sequence in context: A223401 A281480 A170779 * A251903 A253956 A253963

Adjacent sequences: A392330 A392331 A392332 * A392334 A392335 A392336

Keyword

nonn

Author

Chai Wah Wu, Feb 04 2026

Status

approved