A360525 Numbers k such that A360522(k) > 2*k.

30, 42, 60, 66, 70, 78, 84, 90, 102, 114, 120, 126, 132, 138, 140, 150, 156, 168, 174, 180, 186, 204, 210, 222, 228, 246, 252, 258, 276, 282, 294, 300, 318, 330, 348, 354, 360, 366, 372, 390, 402, 420, 426, 438, 444, 462, 474, 492, 498, 510, 516, 534, 546, 564

Offset: 1

Author

Amiram Eldar, Feb 10 2023

Keywords

• nonn

Comments

First differs from A308127 at n = 15.

Analogous to abundant numbers (A005101) with A360522 instead of A000203.

Subsequence of A005101 because A360522(n) <= A000203(n) for all n.

The least odd term is a(1698) = A360526(1) = 15015.

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 8, 95, 1135, 10890, 110867, 1104596, 11048123, 110534517, 1105167384, 11051009278, ... . Apparently, the asymptotic density of this sequence exists and equals 0.1105...

Examples

			30 is a term since A360522(30) = 72 > 2*30.
		

Links

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

Crossrefs

Cf. A000203, A308127, A360522, A360524, A360526.

Subsequence of A005101.

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

Programs

Mathematica

f[p_, e_] := p^e + e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := s[n] > 2*n; Select[Range[1000], q]

PARI

is(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^f[i,2] + f[i,2]) > 2*n;}