A376704 4-brilliant numbers: numbers which are the product of four primes having the same number of decimal digits.

16, 24, 36, 40, 54, 56, 60, 81, 84, 90, 100, 126, 135, 140, 150, 189, 196, 210, 225, 250, 294, 315, 350, 375, 441, 490, 525, 625, 686, 735, 875, 1029, 1225, 1715, 2401, 14641, 17303, 20449, 22627, 24167, 25289, 26741, 28561, 29887, 30613, 31603, 34969, 35321, 36179

Offset: 1

Author

Paolo Xausa, Oct 02 2024

Keywords

• nonn
• base

Examples

			35321 is a term because 35321 = 11 * 13 * 13 * 19, and these four prime factors have the same number of digits.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Dario Alpern, 4-Brilliant Numbers.

Crossrefs

Subsequence of A014613.

Cf. A078972, A376703, A376705, A376706.

Programs

Mathematica

A376704Q[k_] := With[{f = FactorInteger[k]}, Total[f[[All, 2]]] == 4 && Length[Union[IntegerLength[f[[All, 1]]]]] == 1];
Select[Range[40000], A376704Q] (* or *)
dlist4[d_] := Sort[Times @@@ DeleteDuplicates[Map[Sort, Tuples[Prime[Range[PrimePi[10^(d-1)] + 1, PrimePi[10^d]]], 4]]]]; (* Generates terms with d-digits prime factors -- faster but memory intensive *)
Flatten[Array[dlist4, 2]]