Search: id:A091340
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%I A091340
%S A091340 821921625,988676775,4024942087978,4179223134422,100733767393275,
%T A091340 110452715806725
%N A091340 Amicable numbers with property that each member n of the corresponding 
               amicable pair is divisible by sopfr(n) (sopfr: sum of prime factors 
               with repetition).
%C A091340 a(2n),a(2n+1) is a pair of amicable numbers for n=0,1,... For each a(m), 
               m=0,1,...: sopfr(a(m)) divides a(m).
%C A091340 Conjecture: sequence is finite, even though there are quite a lot of 
               known amicable numbers (about 6.0E6 currently).
%H A091340 J.M. Pedersen, <a href="http://amicable.homepage.dk/knwnap.htm">List 
               of known amicable pairs</a>
%H A091340 J. O. M. Pedersen, <a href="http://amicable.homepage.dk/tables.htm">Tables 
               of Aliquot Cycles</a>
%e A091340 a(0): 821921625=3^2*5^3*7*29*59*61, sopfr(n) = 177 = 3*59
%e A091340 a(1): 988676775=3^2*5^2*71*199*311, sopfr(n) = 597 = 3*199
%Y A091340 Cf. A001414.
%Y A091340 Sequence in context: A152156 A017540 A132216 this_sequence A114665 A157798 
               A051470
%Y A091340 Adjacent sequences: A091337 A091338 A091339 this_sequence A091341 A091342 
               A091343
%K A091340 nonn
%O A091340 0,1
%A A091340 Sven Simon (sven-h.simon(AT)t-online.de), Dec 31 2003

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