OFFSET
1,4
COMMENTS
It appears that almost always sigma(n) <= n*sqrt(gamma(n)) (see A358308).
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..10000
MATHEMATICA
a[n_] := Module[{f = FactorInteger[n], p, e}, {p, e} = Transpose[f]; Floor[n * Sqrt[Times @@ p]]- Times @@ ((p^(e+1)-1)/(p-1))]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Apr 25 2024 *)
PROG
(PARI) a(n) = {my(f = factor(n)); floor(n*sqrt(vecprod(f[, 1]))) - sigma(f); } \\ Amiram Eldar, Apr 25 2024
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Dec 09 2022
STATUS
approved