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Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.
2

%I #13 Mar 31 2012 10:24:14

%S 0,0,0,0,1,2,3,5,8,8,12

%N Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.

%C There are infinitely many exponential amicable pairs, for multiplying an exponential amicable pair by a squarefree integer coprime to each of its members will generate another exponential amicable pair. Accordingly, we refer to pairs like (90972,100548) as primitive exponential amicable pairs and to pairs like (454860,502740) that can be obtained from them as nonprimitive. This sequence counts the primitive pairs only.

%D Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-350.

%H Pedersen J. M., <a href="http://amicable.homepage.dk/knwne2.htm">Known exponential amicable pairs</a>.

%e a(7)=3 because there are 3 primitive exponential pairs (m,n) with m<n and m<=10^7

%Y Cf. A051377, A054979, A049419, A054980, A126164, A126165, A126166.

%K hard,nonn

%O 1,6

%A _Ant King_, Dec 21 2006

%E Link corrected and reference added by _Andrew Lelechenko_, Dec 04 2011