OFFSET
1,1
COMMENTS
First differs from A308127 at n = 15.
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...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
30 is a term since A360522(30) = 72 > 2*30.
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]
PROG
(PARI) is(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^f[i, 2] + f[i, 2]) > 2*n; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 10 2023
STATUS
approved