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%I #15 Dec 17 2018 03:13:45
%S 6,42,120,156,420,630,930,1428,1806,2016,2184,3192,4950,5256,8190,
%T 8364,8970,10296,10998,12210,17556,19110,21114,23994,24492,28050,
%U 32640,33306,34362,37506,39270,44310,52326,57684,57840,70686,74256,79800,83076
%N Alexandrian integers: numbers of the form n=pqr such that 1/n = 1/p - 1/q - 1/r for some integers p,q,r.
%C 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
%H Robert Israel, <a href="/A147811/b147811.txt">Table of n, a(n) for n = 1..10000</a>
%H Project Euler, <a href="http://projecteuler.net/index.php?section=problems&id=221">Problem 221: Alexandrian integers</a>
%e 630 is an Alexandrian integer since 630 = 5(-7)(-18) and 1/630 = 1/5 - 1/7 - 1/18.
%p N:= 10^5: # to get all terms <= N
%p 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):
%p sort(convert(A,list)); # _Robert Israel_, Dec 16 2018
%o (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))) }
%Y Cf. A147807, A147808, A147809, A147810.
%K nonn
%O 1,1
%A _M. F. Hasler_ and Alexis Olson (AlexisOlson(AT)gmail.com), Dec 13 2008
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