A088167 Number of earlier occurring divisors of n; a(1)=1.

1, 1, 2, 3, 2, 5, 2, 5, 3, 7, 2, 8, 2, 8, 6, 9, 2, 12, 2, 11, 5, 10, 2, 16, 5, 10, 5, 11, 2, 21, 2, 15, 6, 12, 8, 19, 2, 14, 4, 24, 2, 21, 2, 18, 11, 15, 2, 28, 3, 23, 5, 17, 2, 24, 11, 24, 6, 17, 2, 37, 2, 19, 9, 24, 8, 29, 2, 23, 7, 31, 2, 41, 2, 23, 13, 25, 8, 29, 2, 38, 7, 24, 2, 40

Offset

1,3

Comments

a(n) = #{k: 1<=k<n & n mod a(k) = 0};

a(n)=2 iff n is an odd prime;

a(A088168(n))=n and a(k)<>n for k < A088168(n).

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1; a(n) = [x^n] Sum_{k=1..n-1} x^a(k)/(1 - x^a(k)). - Ilya Gutkovskiy, Dec 11 2017

Maple

A[1]:= 1:
for n from 2 to 1000 do
  A[n]:= numboccur(0, [seq(n mod A[j], j=1..n-1)])
od:
seq(A[n], n=1..1000); # Robert Israel, Sep 20 2015

Mathematica

Fold[Append[#1, Count[#1, x_ /; Divisible[#2, x]]] &, {1}, Range[2, 84]] (* Ivan Neretin, Sep 20 2015 *)

Crossrefs

Cf. A124056 (counting divisors of a(n) instead of those of n).

Sequence in context: A326810 A263726 A328317 * A388264 A073893 A099552

Adjacent sequences: A088164 A088165 A088166 * A088168 A088169 A088170

Keyword

nonn

Author

Reinhard Zumkeller, Sep 21 2003

Status

approved