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A066728 a(n) is the number of integers of the form (n+k+n*k)/(n-k) for k= 1,2,...,n-1. 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n)=1 iff n is 2 or the lesser of twin primes (for n>=3, n follows the sequence A001359).

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

LINKS

Table of n, a(n) for n=1..90.

FORMULA

a(n)=ceil( 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

EXAMPLE

Example: (4+1+4*1)/(4-1); (4+2+4*2)/(4-2); (4+3+4*3)/(4-1) are integers hence a(4)=3.

MAPLE

with(numtheory):A066728 := n->ceil(tau(n*(n+2))/2)-1;

CROSSREFS

Cf. A063091.

Sequence in context: A075148 A210722 A162341 * A279161 A222046 A066899

Adjacent sequences:  A066725 A066726 A066727 * A066729 A066730 A066731

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 15 2002

STATUS

approved

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Last modified May 24 11:23 EDT 2019. Contains 323529 sequences. (Running on oeis4.)