A372384 The smallest composite number k such that the digits of k and its prime factors, both written in base n, contain the same set of distinct digits.

4, 8, 30, 25, 57, 16, 27, 192, 132, 121, 185, 169, 465, 32, 306, 289, 489, 361, 451, 2250, 552, 529, 125, 1586, 81, 1652, 985, 841, 1057, 64, 1285, 86166, 2555, 1332, 1387, 1369, 4752, 3240, 2005, 1681, 2649, 1849, 2047, 5456, 2256, 2209, 343, 5050, 2761, 5876, 2862, 2809, 3097, 15512

Offset: 2

Author

Scott R. Shannon, Apr 29 2024

Keywords

• nonn
• base

Examples

			a(4) = 30 as 30 = 2 * 3 * 5 = 132_4 = 2_4 * 3_4 * 11_4, and both 132_4 and its prime factors contain the same distinct digits 1, 2, and 3.
a(10) = 132 as 132 = 2 * 3 * 11, and both 132 and its prime factors contain the same distinct digits 1, 2, and 3. See also A035141.
a(14) = 465 as 465 = 3 * 5 * 31 = 253_14 = 3_14 * 5_14 * 23_14, and both 253_14 and its prime factors contain the same distinct digits 2, 3, and 5.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 2..404

Crossrefs

Cf. A027746, A035141, A035140, A372309, A371695, A000668.

Formula

a(n) = 2*n + 2 if n = 2^k - 1 with k >= 2, otherwise a(n) = n^2 if n is prime.