%I A007850
%S A007850 30,858,1722,66198,2214408306,24423128562,432749205173838,
%T A007850 14737133470010574,550843391309130318,244197000982499715087866346,
%U A007850 554079914617070801288578559178,1910667181420507984555759916338506
%N A007850 Giuga numbers: numbers n such that p divides n/p - 1 for every prime 
               divisor p of n.
%C A007850 There are no other Giuga numbers with <= 8 prime factors. I did an exhaustive 
               search using a PARI script which implemented Borweins and Girgensohn's 
               method for finding n factor solutions given n-2 factors). - Fred 
               Schneider (frederick.william.schneider(AT)gmail.com), Jul 04 2006
%C A007850 One further Giuga number is known with 10 prime factors, namely:
%C A007850 420001794970774706203871150967065663240419575375163060922876441614\
%C A007850 2557211582098432545190323474818 =
%C A007850 2 * 3 * 11 * 23 * 31 * 47059 * 2217342227 * 1729101023519 * 8491659218261819498490029296021 
               * 58254480569119734123541298976556403
%C A007850 but this may not be the next term. (See the Butske et al. paper.)
%C A007850 Giuga numbers are the solution of the differential equation n'=n+1, being 
               n' the arithmetic derivative of n. [From Paolo P. Lava (ppl(AT)spl.at), 
               Nov 16 2009]
%D A007850 D. Borwein, J. M. Borwein, P. B. Borwein and R. Girgensohn, Giuga's Conjecture 
               on Primality. Amer. Math. Monthly 103, No. 1, 40-50 (1996).
%D A007850 J. M. Borwein and E. Wong, A Survey of Results Relating to Giuga's Conjecture 
               on Primality. Vinet, Luc (ed.): Advances in Mathematical Sciences: 
               CRM's 25 Years. Providence, RI: American Mathematical Society. CRM 
               Proc. Lect. Notes. 11, 13-27 (1997).
%D A007850 Butske, William; Jaje, Lynda M. and Mayernik, Daniel R., On the equation 
               Sum_{p | N} 1/p + (1/N)=1, pseudoperfect numbers and perfectly weighted 
               graphs, Math. Comp. 69 (2000), no. 229, 407-420.
%D A007850 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 30, pp 11, Ellipses, 
               Paris 2008.
%H A007850 Butske, William; Jaje, Lynda M. and Mayernik, Daniel R., <a href="http:/
               /www.ams.org/mcom/2000-69-229/S0025-5718-99-01088-1/S0025-5718-99-01088-1.pdf">
               Pdf version</a>
%H A007850 Mersenne Forum, <a href="http://www.mersenneforum.org/showthread.php?t=4666&highlight=giuga">
               Giuga numbers</a>
%H A007850 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GiugaNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A007850 Wikipedia, <a href="http://en.wikipedia.org/wiki/Agoh-Giuga_conjecture">
               Agoh-Giuga conjecture</a>
%e A007850 1910667181420507984555759916338506 = 2 * 3 * 7 * 43 * 1831 * 138683 * 
               2861051 * 1456230512169437
%Y A007850 Sequence in context: A049394 A143169 A001201 this_sequence A158580 A097313 
               A056389
%Y A007850 Adjacent sequences: A007847 A007848 A007849 this_sequence A007851 A007852 
               A007853
%K A007850 nonn,nice,new
%O A007850 1,1
%A A007850 dborwein(AT)uwo.ca, jborwein(AT)cecm.sfu.ca, pborwein(AT)cecm.sfu.ca 
               and rgirgens(AT)julian.uwo.ca
%E A007850 a(12) from Fred Schneider (frederick.william.schneider(AT)gmail.com), 
               Jul 04 2006
%E A007850 Further references from Fred Schneider (frederick.william.schneider(AT)gmail.com), 
               Aug 19 2006