Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Jun 09 2019 21:15:17
%S 0,1,1,3,1,4,2,4,2,7,1,7,3,5,3,8,1,11,3,7,3,9,2,9,5,7,3,15,1,13,3,6,7,
%T 11,3,11,3,9,3,19,1,15,5,7,5,11,2,17,5,11,3,15,3,19,7,9,3,15,1,15,5,7,
%U 11,15,3,15,3,15,3,29,1,14,5,7,11,15,3,23,4,11,4,15,3,15,7,9,3,29,3,23
%N a(n) is the number of integers of the form (n+k+n*k)/(n-k) for k = 1,2,...,n-1.
%C a(n)=1 iff n is 2 or the lesser of twin primes (for n >= 3, n follows the sequence A001359).
%C Also the number of factors of n*(n+2) which are less than n. - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 02 2003
%F a(n) = ceiling( d(n*(n+2)) / 2 ) - 1, where d(n) = number of divisors of n (A000005). - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 02 2003
%e (4 + 1 + 4*1)/(4 - 1), (4 + 2 + 4*2)/(4 - 2), and (4 + 3 + 4*3)/(4 - 1) are integers, hence a(4)=3.
%p with(numtheory):A066728 := n->ceil(tau(n*(n+2))/2)-1;
%Y Cf. A063091.
%K nonn
%O 1,4
%A _Benoit Cloitre_, Jan 15 2002