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%I #8 Feb 16 2019 21:11:21
%S 100548,968436,5027400,48665232,48421800,468723024,845775504,
%T 938024640,26989110720,40792003200,48200025744,63433162800,
%U 303008547060
%N Larger member of primitive exponential amicable pairs.
%C The lesser counterparts are in A323753.
%C a(14) <= 647935817256.
%H Peter Hagis, Jr., <a href="http://dx.doi.org/10.1155/S0161171288000407">Some Results Concerning Exponential Divisors</a>, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-350.
%H Jan Munch Pedersen, <a href="http://62.198.248.44/aliquot/knwne2.htm">Known Exponential Amicable Pairs</a>.
%e (90972 = 2^2*3^2*7*19^2, 100548 = 2^2*3^3*7^2*19) are a primitive pair since they are an exponential amicable pair (A126165, A126166) and they do not have a common prime divisor with multiplicity 1 in both.
%e (454860, 502740) = 5 * (90972, 100548) are not a primitive pair since 5 divides both of them only once.
%t rad[n_] := Times @@ First /@ FactorInteger[n]; pf[n_] := Denominator[n/rad[n]^2]; esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; es[n_] := esigma[n] - n; s = {}; Do[m = es[n]; If[m > n && es[m] == n && CoprimeQ[pf[n], pf[m]], AppendTo[s, m]], {n, 1, 10^7}]; s (* after _Jean-François Alcover_ at A055231 and A051377 *)
%Y Cf. A051377, A054979, A049419, A054980, A126164, A126165, A126166, A126167, A323753.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Jan 26 2019
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