A034287 -id:A034287 - cp's OEIS frontend

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

Amiram Eldar, Jun 05 2020

nonn

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

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

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

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

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.

A290514 Numbers n such that product of odd divisors of n > product of odd divisors of m for all m < n.

Original entry on oeis.org

1, 3, 5, 7, 9, 15, 21, 27, 33, 35, 39, 45, 63, 75, 99, 105, 135, 165, 189, 195, 225, 315, 495, 525, 585, 675, 693, 735, 765, 819, 825, 855, 945, 1155, 1365, 1485, 1575, 2205, 2475, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8415, 8505, 8775, 8925, 9009, 9135, 9405

Offset: 1

Ilya Gutkovskiy, Aug 04 2017

nonn

Numbers n such that A136655(n) > A136655(m) for all m < n.

Cf. A034287, A034288, A136655, A174572, A182469.

mx = 0; t = {}; Do[u = Product[d, {d, Select[Divisors[n], OddQ[#] &]}]; If[u > mx, mx = u; AppendTo[t, n]], {n, 9500}]; t

cp's OEIS Frontend

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

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