A126165 Smaller member of each exponential amicable pair.

90972, 454860, 937692, 1000692, 1182636, 1546524, 2092356, 2638188, 2820132, 3365964, 3729852, 3911796, 4275684, 4548600, 4688460, 4821516, 5003460, 5367348, 5549292, 5913180, 6095124, 6459012, 6640956, 7186788, 7550676, 7732620, 8096508, 8824284, 9188172, 9370116

Offset: 1

Author

Ant King, Dec 21 2006

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

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

Programs

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, n]], {n, 1, 10^7}]; s (* Amiram Eldar, May 09 2019 *)

Formula

The values of m for which esigma(m)=esigma(n)=m+n and mA051377.

Extensions

More terms from Amiram Eldar, May 09 2019