A078899 Number of times the greatest prime factor of n is the greatest prime factor for numbers <=n; a(1)=1.

1, 1, 1, 2, 1, 2, 1, 3, 3, 2, 1, 4, 1, 2, 3, 4, 1, 5, 1, 4, 3, 2, 1, 6, 5, 2, 7, 4, 1, 6, 1, 5, 3, 2, 5, 8, 1, 2, 3, 7, 1, 6, 1, 4, 8, 2, 1, 9, 7, 9, 3, 4, 1, 10, 5, 8, 3, 2, 1, 10, 1, 2, 9, 6, 5, 6, 1, 4, 3, 10, 1, 11, 1, 2, 11, 4, 7, 6, 1, 12, 12, 2, 1, 11, 5, 2, 3, 8, 1, 13, 7, 4, 3, 2, 5, 13, 1, 12, 9

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2002

Keywords

• nonn
• look

Comments

For n>1: a(n)=1 iff n is prime;

a(n) = n/p for n<=p*(p+1) and p = greatest prime factor of n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A006530, A078898, A078897.

Programs

Maple

p:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= max(numtheory[factorset](n)[]);
      p(t):= p(t)+1
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 09 2015

Mathematica

p[_] = 0; a[1] = 1;
a[n_] := a[n] = Module[{t}, t = FactorInteger[n][[-1, 1]]; p[t] = p[t]+1];
Array[a, 100] (* Jean-François Alcover, Jun 09 2018, after Alois P. Heinz *)

Formula

Ordinal transform of A006530 (Gpf). - Franklin T. Adams-Watters, Aug 28 2006