login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064727 Number of pairs x,y such that 0 < x <= y < n and x+y = n and x*y = kn for some k. 1
0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 3, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 4, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 2, 1, 0, 0, 0, 2, 4, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 1, 5, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

COMMENTS

a(n)=0 when n is a prime or a nonsquare semiprime. Other values of n so that a(n)=0 are 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 210, 222, 230, 231.

When n is a square, a(n) = floor(sqrt(n)/2) and is a record value in the sequence. [corrected by Jon E. Schoenfield, Nov 18 2017]

Number of partitions of n into two parts (s,t) such that (s+t) | s*t. - Wesley Ivan Hurt, Apr 29 2021

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

a(n) = Sum_{i=1..floor(n/2)} (1-ceiling(i*(n-i)/n)+floor(i*(n-i)/n). - Wesley Ivan Hurt, Apr 29 2021

EXAMPLE

a(16) = 2 because 4+12 = 16 and 4*12 = 48 = 3*16, 8+8 = 16 and 8*8 = 4*16.

MAPLE

P:=proc(n) local a, k; a:=0; for k from 1 to trunc(n/2) do

if frac(k*(n-k)/n)=0 then a:=a+1; fi; od; a; end:

seq(P(i), i=1..105); # Paolo P. Lava, Jan 30 2018

MATHEMATICA

Table[Count[IntegerPartitions[n, {2}], _?(Divisible[Apply[Times, #], n] &)], {n, 105}] (* Michael De Vlieger, Nov 18 2017 *)

PROG

(PARI) A064727(n) = { my(s=0); for(x=1, n, y = (n-x); if((x<=y)&&(0==((x*y)%n)), s++)); (s); }; \\ Antti Karttunen, Nov 18 2017

CROSSREFS

Sequence in context: A158971 A121467 A071325 * A343222 A112378 A324832

Adjacent sequences:  A064724 A064725 A064726 * A064728 A064729 A064730

KEYWORD

nonn,look

AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 14 2001

EXTENSIONS

Offset corrected (to 1) by Antti Karttunen, Nov 18 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 09:05 EDT 2021. Contains 347518 sequences. (Running on oeis4.)