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A239585 Prime factor <= other prime factor of n-th brilliant number, cf. A078972.

%I A239585 #24 Oct 10 2024 15:29:43
%S A239585 2,2,3,2,2,3,3,5,5,7,11,11,13,11,11,13,13,11,17,13,11,17,11,19,13,17,
%T A239585 13,11,19,11,11,13,17,11,17,23,13,19,13,11,19,13,17,11,23,11,13,17,19,
%U A239585 23,17,11,13,19,11,13,17,11,19,29,23,11,13,19,29,17,11
%N A239585 Prime factor <= other prime factor of n-th brilliant number, cf. A078972.
%C A239585 a(n) = A020639(A078972(n)) = A078972(n) / A239586(n).
%C A239585 A055642(a(n)) = A055642(A239586(n)).
%H A239585 Reinhard Zumkeller, <a href="/A239585/b239585.txt">Table of n, a(n) for n = 1..20000</a>
%H A239585 Dario Alpern, <a href="https://www.alpertron.com.ar/BRILLIANT.HTM">Brilliant Numbers</a>
%e A239585       n  | A239585(n) | A239586(n) | A078972(n)   Lengths of factors
%e A239585   -------+------------+------------+-----------   ------------------
%e A239585       1  |        2   |        2   |        4          1
%e A239585       5  |        2   |        7   |       14
%e A239585      10  |        7   |        7   |       49
%e A239585          |.........................|              ..................
%e A239585      11  |       11   |       11   |      121          2
%e A239585      78  |       11   |       97   |     1067
%e A239585     100  |       37   |       37   |     1369
%e A239585     241  |       97   |       97   |     9409
%e A239585          |.........................|              ..................
%e A239585     242  |      101   |      101   |    10201          3
%e A239585    1000  |      193   |      263   |    50759
%e A239585    2530  |      101   |      997   |   100697
%e A239585   10000  |      743   |      937   |   696191
%e A239585   10537  |      997   |      997   |   994009
%e A239585          |.........................|              ..................
%e A239585   10538  |     1009   |     1009   |  1018081          4
%t A239585 Table[With[{f = FactorInteger[k]}, If[Total[f[[All, 2]]] == 2 && Length[Union[IntegerLength[f[[All, 1]]]]] == 1, f[[1, 1]], Nothing]], {k, 1000}] (* _Paolo Xausa_, Oct 02 2024 *)
%t A239585 dlist2[d_] := Union[Times @@@ Tuples[Prime[Range[PrimePi[10^(d-1)] + 1, PrimePi[10^d]]], 2]]; (* Generates terms with d-digits prime factors -- faster but memory intensive *)
%t A239585 Map[FactorInteger[#][[1, 1]]&, Flatten[Array[dlist2, 2]]] (* _Paolo Xausa_, Oct 09 2024 *)
%o A239585 (Haskell)
%o A239585 a239585 = a020639 . a078972
%Y A239585 Subsequence of A084126.
%Y A239585 Cf. A020639, A055642, A078972, A239586.
%K A239585 nonn,look,base
%O A239585 1,1
%A A239585 _Reinhard Zumkeller_, Mar 22 2014