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

1,1

Comments

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

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..20000

Dario Alpern, Brilliant Numbers

Example

      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

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 *)

Prog

(Haskell)
a239585 = a020639 . a078972

Crossrefs

Subsequence of A084126.

Cf. A020639, A055642, A078972, A239586.

Sequence in context: A153095 A254574 A306991 * A321788 A182093 A254618

Adjacent sequences: A239582 A239583 A239584 * A239586 A239587 A239588

Keyword

nonn,look,base

Author

Reinhard Zumkeller, Mar 22 2014

Status

approved