A336672 Unitary barely 3-deficient numbers: numbers m such that usigma(k)/k < usigma(m)/m < 3 for all numbers k < m, where usigma is the sum of unitary divisors function (A034448).

1, 2, 6, 30, 210, 2310, 110670, 182910, 898590, 22851570, 26266170, 45255210, 64124970, 265402410, 1374105810, 1631268870

Offset: 1

Author

Amiram Eldar, Jul 29 2020

Keywords

• nonn
• more

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.

Crossrefs

The unitary version of A307122.

Cf. A034448, A129487, A285615, A302572, A336671.

Programs

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