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Prime factor <= other prime factor of n-th brilliant number, cf. A078972.
3

%I #24 Oct 10 2024 15:29:43

%S 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 13,11,19,11,11,13,17,11,17,23,13,19,13,11,19,13,17,11,23,11,13,17,19,

%U 23,17,11,13,19,11,13,17,11,19,29,23,11,13,19,29,17,11

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

%C a(n) = A020639(A078972(n)) = A078972(n) / A239586(n).

%C A055642(a(n)) = A055642(A239586(n)).

%H Reinhard Zumkeller, <a href="/A239585/b239585.txt">Table of n, a(n) for n = 1..20000</a>

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

%e n | A239585(n) | A239586(n) | A078972(n) Lengths of factors

%e -------+------------+------------+----------- ------------------

%e 1 | 2 | 2 | 4 1

%e 5 | 2 | 7 | 14

%e 10 | 7 | 7 | 49

%e |.........................| ..................

%e 11 | 11 | 11 | 121 2

%e 78 | 11 | 97 | 1067

%e 100 | 37 | 37 | 1369

%e 241 | 97 | 97 | 9409

%e |.........................| ..................

%e 242 | 101 | 101 | 10201 3

%e 1000 | 193 | 263 | 50759

%e 2530 | 101 | 997 | 100697

%e 10000 | 743 | 937 | 696191

%e 10537 | 997 | 997 | 994009

%e |.........................| ..................

%e 10538 | 1009 | 1009 | 1018081 4

%t 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 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 Map[FactorInteger[#][[1, 1]]&, Flatten[Array[dlist2, 2]]] (* _Paolo Xausa_, Oct 09 2024 *)

%o (Haskell)

%o a239585 = a020639 . a078972

%Y Subsequence of A084126.

%Y Cf. A020639, A055642, A078972, A239586.

%K nonn,look,base

%O 1,1

%A _Reinhard Zumkeller_, Mar 22 2014