A328134 Exponential highly abundant numbers: numbers m such that esigma(m) > esigma(k) for all k < m, where esigma(m) is the sum of exponential divisors of m (A051377).

1, 2, 3, 4, 7, 8, 9, 12, 16, 18, 20, 28, 36, 52, 60, 68, 72, 84, 92, 100, 124, 132, 140, 144, 180, 244, 252, 300, 324, 360, 396, 468, 588, 612, 684, 828, 900, 1116, 1260, 1332, 1476, 1548, 1692, 1764, 2124, 2196, 2340, 2412, 2556, 2628, 2700, 2772, 2844, 2988

Offset: 1

Author

Amiram Eldar, Oct 04 2019

Keywords

• nonn

Comments

The exponential version of A002093.

Examples

			The first 10 values of esigma(k) for k = 1 to 10 are 1, 2, 3, 6, 5, 6, 7, 10, 12, 10. The record values are reached for 1, 2, 3, 4, 7, 8, 9.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002093, A051377, A285614 (unitary), A292983 (bi-unitary), A327634 (infinitary).

Programs

Mathematica

f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; s = {}; em = 0; Do[e = esigma[n]; If[e > em, em = e; AppendTo[s, n]], {n, 1, 3000}]; s