A357607 Odd numbers k such that A162296(k) > 2*k.

4725, 6615, 7875, 8505, 11025, 14175, 15435, 17325, 19845, 20475, 22275, 23625, 24255, 25515, 26775, 28665, 29925, 31185, 33075, 36225, 36855, 37125, 37485, 38115, 39375, 40425, 41895, 42525, 46305, 47775, 48195, 50715, 51975, 53235, 53865, 55125, 57915, 59535

Offset

1,1

Comments

The least term that is not divisible by 3 is a(89047132) = 134785275625.

The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 4, 60, 640, 6650, 66044, 660230, 6604594, 66073470, ... . Apparently, the asymptotic density of this sequence exists and equals 0.000660... .

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4725 is a term since it is odd, and A162296(4725) = 9728 > 2*4725.

Mathematica

q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) > 2*n]; Select[Range[3, 60000, 2], q]

Crossrefs

Cf. A162296.

Subsequence of A005231, A013929 and A357605.

Similar sequences: A094889, A127666, A129485, A293186, A321147, A348275, A348605.

Sequence in context: A252239 A234086 A093789 * A252226 A252204 A374502

Adjacent sequences: A357604 A357605 A357606 * A357608 A357609 A357610

Keyword

nonn

Author

Amiram Eldar, Oct 06 2022

Status

approved