A357605 Numbers k such that A162296(k) > 2*k.

36, 48, 72, 80, 96, 108, 120, 144, 160, 162, 168, 180, 192, 200, 216, 224, 240, 252, 264, 270, 280, 288, 300, 312, 320, 324, 336, 352, 360, 378, 384, 392, 396, 400, 408, 416, 432, 448, 450, 456, 468, 480, 486, 500, 504, 528, 540, 552, 560, 576, 588, 594, 600, 612

Offset: 1

Author

Amiram Eldar, Oct 06 2022

Keywords

• nonn

Comments

The least odd term is a(470) = A357607(1) = 4725.

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 5, 92, 1011, 10160, 102125, 1022881, 10231151, 102249758, 1022781199, 10229781638, ... . Apparently, the asymptotic density of this sequence exists and equals 0.102... .

An analog of abundant numbers, in which the divisor sum is restricted to nonsquarefree divisors. - Peter Munn, Oct 26 2022

Examples

			36 is a term since A162296(36) = 79 > 2*36.
		

Links

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

Crossrefs

Cf. A162296.

Subsequence of A005101 and A013929.

Similar sequences: A034683, A064597, A129575, A129656, A292982, A348274, A348604.

Programs

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[2, 1000], q]