A126166 Larger member of each exponential amicable pair.

100548, 502740, 968436, 1106028, 1307124, 1709316, 2312604, 2915892, 3116988, 3720276, 4122468, 4323564, 4725756, 5027400, 4842180, 5329044, 5530140, 5932332, 6133428, 6535620, 6736716, 7138908, 7340004, 7943292, 8345484, 8546580, 8948772, 9753156, 10155348

Offset

1,1

Comments

This sequence includes the largest member of all exponential amicable pairs and does not discriminate between primitive and nonprimitive pairs.

References

Hagis, Peter Jr.; Some Results Concerning Exponential Divisors, Internat. J. Math. & Math. Sci., Vol. 11, No. 2, (1988), pp. 343-350.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Peter Hagis, Jr., Some results concerning exponential divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-349.

Ant King, Mathematica programs for A126164 - A126166

David Moews, Perfect, amicable and sociable numbers.

J. M. Pedersen, Known exponential amicable pairs.

Formula

The values of n for which esigma(m)=esigma(n)=m+n and m<n, where esigma is defined in A051377

Example

a(3)= 968436 because (937692,968436) is the third exponential amicable pair

Mathematica

fun[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ fun @@@ FactorInteger[n]; s = {}; Do[m = esigma[n] - n; If[m > n && esigma[m] - m == n, AppendTo[s, m]], {n, 1, 10^7}]; s (* Amiram Eldar, May 09 2019 *)

Crossrefs

Cf. A126165, A051377, A054979, A049419, A054980, A126164.

Sequence in context: A365375 A235901 A251171 * A323754 A251042 A117091

Adjacent sequences: A126163 A126164 A126165 * A126167 A126168 A126169

Keyword

nonn

Author

Ant King, Dec 21 2006

Extensions

Link corrected and reference added by Andrew Lelechenko, Dec 04 2011

More terms from Amiram Eldar, May 09 2019

Status

approved