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Number of amicable pairs with lesser member at most 2^n.
1

%I #25 Dec 13 2020 05:14:53

%S 0,0,0,0,0,0,0,1,1,1,2,3,5,7,8,9,16,22,30,42,57,68,95,133,167,205,257,

%T 342,460,605,786,1043,1356,1749,2294,2905,3757,4811,6181,7893,10146,

%U 13051,16762,21396,27380,34939,44449,56481,71453,90783,115200,145702,184045,232899,294326,372216

%N Number of amicable pairs with lesser member at most 2^n.

%C Sergei Chernykh led a BOINC project to find a(64) = 2390655. The project took 7 months and used several hundred CPU-years of computation time.

%H Amiram Eldar, <a href="/A290985/b290985.txt">Table of n, a(n) for n = 1..66</a> (calculated from Chernykh's database)

%H Sergei Chernykh, <a href="https://sech.me/boinc/Amicable/">Amicable Numbers</a>.

%o (PARI) has(n,f=factor(n))=my(t=sigma(f)-n); t>n && sigma(t)==n+t

%o a(n)=my(s); forfactored(k=1,2^n, if(has(k[1],k[2]), s++)); s

%Y Cf. A002025, A066873, A259180.

%K nonn,hard

%O 1,11

%A _Charles R Greathouse IV_, Aug 16 2017