login
Numbers where records occur for the product of exponential divisors function (A157488).
1

%I #40 Jun 06 2020 03:19:13

%S 1,2,3,4,8,9,12,16,20,28,36,72,100,144,324,400,576,900,1764,2700,3528,

%T 3600,7056,10800,14400,28224,32400,44100,88200,108900,129600,176400,

%U 396900,435600,608400,705600,1587600,3920400,5336100,5475600,6350400,14288400,15681600

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

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

%H Amiram Eldar, <a href="/A332622/b332622.txt">Table of n, a(n) for n = 1..68</a> (terms below 10^10)

%F 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.

%t 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

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Jun 05 2020