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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. 3
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. - M. F. Hasler, Jan 07 2009

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

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.

MAPLE

N:= 10^5: # to get all terms <= N

A:= select(`<=`, {seq(seq(p*(p+d)*(p+(p^2+1)/d), d=numtheory:-divisors(p^2+1)), p=1..floor(N^(1/3)))}, N):

sort(convert(A, list)); # Robert Israel, Dec 16 2018

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

Cf. A147807, A147808, A147809, A147810.

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

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)