

A066728


a(n) is the number of integers of the form (n+k+n*k)/(nk) for k = 1,2,...,n1.


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
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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) = 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


EXAMPLE

(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.


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



