OFFSET
1,1
COMMENTS
The least odd term is a(224) = A357697(1) = 1575.
The lower asymptotic density of this sequence is larger than 12/(91*zeta(3)) = 0.1097... which is the density of its subsequence of cubefree numbers larger than 6 and divisible by 6.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 13, 143, 1440, 14470, 144187, 1442500, 14426015, 144267400, 1442567879, 14425142573, ... . Apparently, the asymptotic density of this sequence exists and equals 0.1442... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
12 = 2^2 * 3 is a term since it is cubefree and sigma(12) = 28 > 2*12.
MATHEMATICA
f[p_, e_] := (p^(e+1)-1)/(p-1); q[1] = 0; q[n_] := AllTrue[(fct = FactorInteger[n])[[;; , 2]], # < 3 &] && Times @@ f @@@ fct > 2*n; Select[Range[400], q]
PROG
(PARI) is(n) = {my(f = factor(n)); (n==1 || vecmax(f[, 2]) < 3) && sigma(f, -1) > 2};
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 10 2022
STATUS
approved