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A126165
Smaller member of each exponential amicable pair.
12
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
1,1
COMMENTS
This sequence includes the smallest member of all exponential amicable pairs and does not discriminate between primitive and nonprimitive pairs.
LINKS
Peter Hagis, Jr., Some results concerning exponential divisors, International Journal of Mathematics and Mathematical Sciences, Vol. 11, No. 2, (1988), pp. 343-349.
FORMULA
The values of m for which esigma(m)=esigma(n)=m+n and m<n, where esigma is defined in A051377.
EXAMPLE
a(3)=937692 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, n]], {n, 1, 10^7}]; s (* Amiram Eldar, May 09 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ant King, Dec 21 2006
EXTENSIONS
More terms from Amiram Eldar, May 09 2019
STATUS
approved