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

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, 13, 11, 19, 11, 11, 13, 17, 11, 17, 23, 13, 19, 13, 11, 19, 13, 17, 11, 23, 11, 13, 17, 19, 23, 17, 11, 13, 19, 11, 13, 17, 11, 19, 29, 23, 11, 13, 19, 29, 17, 11

Offset: 1

Author

Reinhard Zumkeller, Mar 22 2014

Keywords

• nonn
• look
• base

Comments

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

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

Examples

			      n  | A239585(n) | A239586(n) | A078972(n)   Lengths of factors
  -------+------------+------------+-----------   ------------------
      1  |        2   |        2   |        4          1
      5  |        2   |        7   |       14
     10  |        7   |        7   |       49
         |.........................|              ..................
     11  |       11   |       11   |      121          2
     78  |       11   |       97   |     1067
    100  |       37   |       37   |     1369
    241  |       97   |       97   |     9409
         |.........................|              ..................
    242  |      101   |      101   |    10201          3
   1000  |      193   |      263   |    50759
   2530  |      101   |      997   |   100697
  10000  |      743   |      937   |   696191
  10537  |      997   |      997   |   994009
         |.........................|              ..................
  10538  |     1009   |     1009   |  1018081          4
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..20000
• Dario Alpern, Brilliant Numbers

Crossrefs

Subsequence of A084126.

Cf. A020639, A055642, A078972, A239586.

Programs

Haskell

a239585 = a020639 . a078972

Mathematica

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 *)
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 *)
Map[FactorInteger[#][[1, 1]]&, Flatten[Array[dlist2, 2]]] (* Paolo Xausa, Oct 09 2024 *)