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

0,2

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

Formula

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

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);

Crossrefs

Cf. A003415.

Sequence in context: A243546 A243554 A361734 * A260438 A112197 A112198

Adjacent sequences: A263108 A263109 A263110 * A263112 A263113 A263114

Keyword

nonn

Author

Alois P. Heinz, Oct 09 2015

Status

approved