cp's OEIS Frontend

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

%I A088167 #17 Dec 11 2017 14:28:19
%S A088167 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,
%T A088167 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,
%U A088167 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
%N A088167 Number of earlier occurring divisors of n; a(1)=1.
%C A088167 a(n) = #{k: 1<=k<n & n mod a(k) = 0};
%C A088167 a(n)=2 iff n is an odd prime;
%C A088167 a(A088168(n))=n and a(k)<>n for k < A088168(n).
%H A088167 Ivan Neretin, <a href="/A088167/b088167.txt">Table of n, a(n) for n = 1..10000</a>
%F A088167 a(1) = 1; a(n) = [x^n] Sum_{k=1..n-1} x^a(k)/(1 - x^a(k)). - _Ilya Gutkovskiy_, Dec 11 2017
%p A088167 A[1]:= 1:
%p A088167 for n from 2 to 1000 do
%p A088167   A[n]:= numboccur(0, [seq(n mod A[j],j=1..n-1)])
%p A088167 od:
%p A088167 seq(A[n],n=1..1000); # _Robert Israel_, Sep 20 2015
%t A088167 Fold[Append[#1, Count[#1, x_ /; Divisible[#2, x]]] &, {1}, Range[2, 84]] (* _Ivan Neretin_, Sep 20 2015 *)
%Y A088167 Cf. A124056 (counting divisors of a(n) instead of those of n).
%K A088167 nonn
%O A088167 1,3
%A A088167 _Reinhard Zumkeller_, Sep 21 2003