OFFSET
1,1
COMMENTS
First differs from A333950 at n = 1258. Terms that are not in A333950 include 8564325, 8565795, 8567325, ... and terms of A333950 that are not here include 1126125, 2096325, 2207205, ... .
The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 16, 125, 1127, 11734, 116911, 1162781, 11638566, 116342286, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00116... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1575 = 3^2 * 5^2 * 7 is a term since it is odd and cubefree and sigma(1575) = 3224 > 2*1575.
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[1, 30000, 2], q]
PROG
(PARI) is(n) = {my(f); if(n%2 == 0, return(0)); f = factor(n); (n==1 || vecmax(f[, 2]) < 3) && sigma(f, -1) > 2};
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 10 2022
STATUS
approved