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

1,2

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)

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.

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

Crossrefs

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

Sequence in context: A032883 A023786 A018231 * A085256 A364810 A335761

Adjacent sequences: A332619 A332620 A332621 * A332623 A332624 A332625

Keyword

nonn

Author

Amiram Eldar, Jun 05 2020

Status

approved