A376158 Numbers k having two prime divisors p < q such that p! <= k <= q!.

6, 10, 14, 15, 20, 21, 22, 26, 28, 30, 33, 34, 38, 39, 40, 42, 44, 45, 46, 50, 51, 52, 56, 57, 58, 60, 62, 63, 66, 68, 69, 70, 74, 75, 76, 78, 80, 82, 84, 86, 87, 88, 90, 92, 93, 94, 98, 99, 100, 102, 104, 105, 106, 110, 111, 112, 114, 116, 117, 118, 120, 122, 123, 124, 126, 129, 130, 132, 134, 136, 138, 140, 141, 142, 145

Offset: 1

Author

Mike Jones, Sep 12 2024

Keywords

• nonn

Comments

Different from A330136.

Examples

			40 is in the list because 40 has at least 2 distinct prime divisors, and the smallest prime divisor of 40 is 2 and the largest prime divisor of 40 is 5, and 2! <= 40 <= 5! because 2! = 2 and 5! = 120.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020639, A006530, A330136.

Programs

Maple

q:= n-> (s-> nops(s)>1 and min(s)!<=n and n<=max(s)!)(numtheory[factorset](n)):
select(q, [$2..150])[];  # Alois P. Heinz, Sep 20 2024

Mathematica

q[k_] := Module[{p = FactorInteger[k][[;; , 1]]}, Length[p] > 1 && k >= p[[1]]! && k <= p[[-1]]!]; Select[Range[125], q] (* Amiram Eldar, Sep 20 2024 *)