A323754 Larger member of primitive exponential amicable pairs.

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

Offset

1,1

Comments

The lesser counterparts are in A323753.

a(14) <= 647935817256.

Links

Table of n, a(n) for n=1..13.

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.

Example

(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.

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 *)

Crossrefs

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

Sequence in context: A235901 A251171 A126166 * A251042 A117091 A184788

Adjacent sequences: A323751 A323752 A323753 * A323755 A323756 A323757

Keyword

nonn,more

Author

Amiram Eldar, Jan 26 2019

Status

approved