A332622 Numbers where records occur for the product of exponential divisors function (A157488).

1, 2, 3, 4, 8, 9, 12, 16, 20, 28, 36, 72, 100, 144, 324, 400, 576, 900, 1764, 2700, 3528, 3600, 7056, 10800, 14400, 28224, 32400, 44100, 88200, 108900, 129600, 176400, 396900, 435600, 608400, 705600, 1587600, 3920400, 5336100, 5475600, 6350400, 14288400, 15681600

Offset: 1

Author

Amiram Eldar, Jun 05 2020

Keywords

• nonn

Comments

The corresponding record values are 1, 2, 3, 8, 16, 27, 72, 128, 200, 392, 46656, 186624, 1000000, ...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..68 (terms below 10^10)

Crossrefs

Cf. A034287, A061742, A157488, A328134, A318278, A322791.

Programs

Mathematica

f[p_, e_] := p^(DivisorSigma[1, e]/DivisorSigma[0, e]); exprod[n_] := (Times @@ (f @@@ (fct = FactorInteger[n])))^(Times @@ DivisorSigma[0, Last /@ fct]); em = 0; s = {}; Do[If[(e = exprod[n]) > em, em = e; AppendTo[s, n]], {n, 1, 10^6}]; s

Formula

The first 8 terms of A157488 are 1, 2, 3, 8, 5, 6, 7 and 16. The record values occur at 1, 2, 3, 4 and 8 - the first 5 terms of this sequence.