1,1

Union of A126165 and A126166. The first 10 terms of this sequence are the same as the first 10 terms of A127660.

The asymptotic density of this sequence is Sum_{n>=1} (f(A323753(n)) + f(A323754(n))) = 5.94917...*10^(-6), where f(n) = (6/(Pi^2*n)) * Product_{prime p|n} (p/(p+1)). - Amiram Eldar, Dec 05 2025

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.

J. O. M. Pedersen, Tables of Aliquot Cycles.

J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]

J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

Non-e-perfect numbers for which A126164(A126164(n)) = n.

a(5) = 937692 because the fifth non-e-perfect integer that satisfies A126164(A126164(n)) = n is 937692.

ExponentialDivisors[1]={1}; ExponentialDivisors[n_]:=Module[{}, {pr, pows}=Transpose@FactorInteger[n]; divpowers=Distribute[Divisors[pows], List]; Sort[Times@@(pr^Transpose[divpowers])]]; se[n_]:=Plus@@ExponentialDivisors[n]-n; g[n_] := If[n > 0, se[n], 0]; eTrajectory[n_] := Most[NestWhileList[g, n, UnsameQ, All]]; ExponentialAmicableNumberQ[k_]:=If[Nest[se, k, 2]==k && !se[k]==k, True, False]; Select[Range[5 10^6], ExponentialAmicableNumberQ[ # ] &]

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, 10^6}]; s (* Amiram Eldar, May 09 2019 *)

Cf. A126164, A126165, A126166, A127656, A127657, A127658, A127660, A051377, A323753, A323754.

Sequence in context: A015316 A212853 A127660 * A126165 A323753 A255985

Adjacent sequences: A127656 A127657 A127658 * A127660 A127661 A127662

Ant King, Jan 25 2007

Link corrected by Andrew Lelechenko, Dec 04 2011

More terms from Amiram Eldar, May 09 2019

approved