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A323754
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Larger member of primitive exponential amicable pairs.
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1
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100548, 968436, 5027400, 48665232, 48421800, 468723024, 845775504, 938024640, 26989110720, 40792003200, 48200025744, 63433162800, 303008547060
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OFFSET
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1,1
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COMMENTS
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The lesser counterparts are in A323753.
a(14) <= 647935817256.
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LINKS
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EXAMPLE
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(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.
(454860, 502740) = 5 * (90972, 100548) are not a primitive pair since 5 divides both of them only once.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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