A066728 - 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