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4-brilliant numbers: numbers which are the product of four primes having the same number of decimal digits.
7

%I #25 Oct 08 2024 18:38:33

%S 16,24,36,40,54,56,60,81,84,90,100,126,135,140,150,189,196,210,225,

%T 250,294,315,350,375,441,490,525,625,686,735,875,1029,1225,1715,2401,

%U 14641,17303,20449,22627,24167,25289,26741,28561,29887,30613,31603,34969,35321,36179

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

%H Paolo Xausa, <a href="/A376704/b376704.txt">Table of n, a(n) for n = 1..10000</a>

%H Dario Alpern, <a href="https://www.alpertron.com.ar/BRILLIANT4.HTM">4-Brilliant Numbers</a>.

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

%t A376704Q[k_] := With[{f = FactorInteger[k]}, Total[f[[All, 2]]] == 4 && Length[Union[IntegerLength[f[[All, 1]]]]] == 1];

%t Select[Range[40000], A376704Q] (* or *)

%t 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 *)

%t Flatten[Array[dlist4, 2]]

%Y Subsequence of A014613.

%Y Cf. A078972, A376703, A376705, A376706.

%K nonn,base

%O 1,1

%A _Paolo Xausa_, Oct 02 2024