login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A147811 Alexandrian integers: numbers of the form n=pqr such that 1/n = 1/p-1/q-1/r for some integers p,q,r. 2
6, 42, 120, 156, 420, 630, 930, 1428, 1806, 2016, 2184, 3192, 4950, 5256, 8190, 8364, 8970, 10296, 10998, 12210, 17556, 19110, 21114, 23994, 24492, 28050, 32640, 33306, 34362, 37506, 39270, 44310, 52326, 57684, 57840, 70686, 74256, 79800, 83076 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The numbers are of the form p(p+d)(p+(p^2+1)/d), where d runs over divisors of p^2+1 and p runs over all positive integers. See also A147807-A147810. [From M. F. Hasler, Jan 07 2009]

LINKS

Table of n, a(n) for n=1..39.

Project Euler, Problem 221: Alexandrian integers

EXAMPLE

630 is an Alexandrian integer since 630 = 5(-7)(-18) and 1/630 = 1/5 - 1/7 - 1/18.

PROG

(PARI) is_A147811(n) = { my(d=divisors(n), c=#d+1); n<42 && return(n==6); for( i=2, c-3, d[i+1]^2>d[c-i] && return; d[c-i]%d[i]==1 | next; for( j=i+1, c-i, d[j]^2>d[c-i] && next(2); d[c-i]\d[j]*(d[j]-d[i]) == d[j]*d[i]+1 && return(1))) }

CROSSREFS

Sequence in context: A153786 A256833 A164016 * A046763 A199905 A176780

Adjacent sequences:  A147808 A147809 A147810 * A147812 A147813 A147814

KEYWORD

nonn

AUTHOR

M. F. Hasler and Alexis Olson (AlexisOlson(AT)gmail.com), Dec 13 2008

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 00:12 EST 2018. Contains 317332 sequences. (Running on oeis4.)