A387093 Composite numbers that contain only prime digits and whose prime factors contain only prime digits.

25, 27, 32, 35, 72, 75, 222, 225, 252, 322, 333, 375, 525, 552, 555, 575, 735, 777, 2352, 2553, 2555, 2775, 3357, 3375, 3552, 3577, 5222, 5352, 5575, 7252, 7322, 23253, 23373, 23532, 23535, 23552, 25275, 25725, 25737, 27232, 27252, 27375, 32352, 32375

Offset: 1

Author

Scott R. Shannon and Ursula Ponting, Aug 16 2025

Keywords

• nonn
• base

Examples

			25725 is a term as 25725 = 3 * 5^2 * 7^3, and both the number and its prime factors only contain prime digits.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..2298 (all terms < 10^12).

Crossrefs

Cf. A061371, A027746, A000040, A019546.

Programs

Mathematica

Select[Select[Range[33000], CompositeQ], And[AllTrue[Union@ IntegerDigits[#], PrimeQ], AllTrue[Union@ Flatten@ Map[IntegerDigits, FactorInteger[#][[All, 1]] ], PrimeQ]] &] (* Michael De Vlieger, Aug 16 2025 *)