OFFSET
1,2
COMMENTS
Unitary 3-deficient numbers are numbers k such that usigma(k) < 3*k, i.e., numbers that are not in A285615.
The corresponding values of usigma(m)/m are 1, 1.5, 2, 2.4, 2.742..., 2.992..., ...
Are terms squarefree? At some point, do we know that a(n) is divisible by primorial(k) for all n > N(k) for some N(k)? - David A. Corneth, Jul 29 2020
Not all the terms are squarefree. E.g., a(12) = 45255210 is divisible by 11^2.
MATHEMATICA
usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); s = {}; rm = 0; Do[r = usigma[n]/n; If[r < 3 && r > rm, rm = r; AppendTo[s, n]], {n, 1, 10^5}]; s
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Jul 29 2020
STATUS
approved