OFFSET
1,2
COMMENTS
It appears that if sigma(m) > m*sqrt(gamma(m)) then m must be even, and that almost always sigma(m) <= m*sqrt(gamma(m)) (see also A358309).
Is there a simpler alternative description of the terms of the present sequence?
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 77, section III.1.1.d.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..400
MATHEMATICA
q[k_] := Module[{f = FactorInteger[2*k], p, e}, {p, e} = Transpose[f]; Times @@ ((p^(e+1)-1)/(p-1)) > 2*k*Sqrt[Times @@ p]]; Select[Range[10^4], q] (* Amiram Eldar, Apr 25 2024 *)
PROG
(PARI) is(k) = {my(f = factor(2*k)); sigma(f)^2 > 4 * k^2 * vecprod(f[, 1]); } \\ Amiram Eldar, Apr 25 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 09 2022
STATUS
approved