A263111 Ordinal transform of the arithmetic derivative A003415.

1, 2, 1, 2, 1, 3, 1, 4, 1, 1, 1, 5, 1, 6, 1, 1, 1, 7, 1, 8, 1, 1, 1, 9, 1, 2, 1, 1, 2, 10, 1, 11, 1, 1, 1, 2, 1, 12, 2, 2, 1, 13, 1, 14, 1, 1, 1, 15, 1, 2, 1, 1, 1, 16, 1, 3, 1, 1, 2, 17, 2, 18, 1, 1, 1, 1, 1, 19, 1, 1, 1, 20, 1, 21, 2, 1, 2, 2, 1, 22, 1, 1

Offset: 0

Author

Alois P. Heinz, Oct 09 2015

Keywords

• nonn

Comments

n is the a(n)-th nonnegative integer having its arithmetic derivative.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A003415.

Programs

Maple

p:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= n*add(i[2]/i[1], i=ifactors(n)[2]);
      p(t):= p(t)+1
    end:
seq(a(n), n=0..100);

Formula

a(n) = |{ j in {0..n} : A003415(j) = A003415(n) }|.