A323754 Larger member of primitive exponential amicable pairs.

100548, 968436, 5027400, 48665232, 48421800, 468723024, 845775504, 938024640, 26989110720, 40792003200, 48200025744, 63433162800, 303008547060

Offset: 1

Author

Amiram Eldar, Jan 26 2019

Keywords

• nonn
• more

Comments

The lesser counterparts are in A323753.

a(14) <= 647935817256.

Examples

			(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.
		

Links

• Peter Hagis, Jr., Some Results Concerning Exponential Divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-350.
• Jan Munch Pedersen, Known Exponential Amicable Pairs.

Crossrefs

Cf. A051377, A054979, A049419, A054980, A126164, A126165, A126166, A126167, A323753.

Programs

Mathematica

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 *)