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%I #2 Mar 30 2012 17:22:56
%S 0,2,1,7,3,3,2,7,1,8,4,8,7,5,6,15,4,9,9,14,8,15,8,15
%N Number of amicable pairs of the form (2^n * pq, 2^n * rs), where p, q, r, and s are distinct odd primes.
%C There are only a finite number of such pairs for each n. A180330(n) is the smallest value of 2^n * pq which is part of an amicable pair. The terms in this sequence equal the count of such amicable pairs in Pedersen's table up to n=22, after which the table stops being a complete list of all amicable pairs of the form 2^n * pq. Currently, Pedersen's table lists 4 such amicable pairs for n=23 when there are actually 8 pairs.
%H J. M. Pedersen, <a href="http://amicable.adsl.dk/aliquot/apstat/apreg22.txt">Regular type (2,2) amicable pairs</a>
%e Eight pairs for n=23, with new ones indicated by *:
%e (112072375885373577887744, 112072384861110016147456) *
%e (1268674663237438821892096, 1268674685089131637243904)
%e (207428765646084356836425728, 207428778650058836339064832) *
%e (3201546606177940316018966528, 3201546948253280471426793472)
%e (3246126368411500102994100224, 3246126753752370852634034176)
%e (30886958374694867104144818176, 30886959839775761339382759424) *
%e (58230121837690366602703273984, 58230128772645945195748130816)
%e (1564092755993481057609717907456, 1564092823984266648474085228544) *
%Y Cf. A180650, A180651 (the amicable pairs for each n)
%K hard,nonn
%O 1,2
%A _T. D. Noe_, Sep 25 2010