A285615 Numbers k such that usigma(k) >= 3*k, where usigma(k) = sum of unitary divisors of k (A034448).

30030, 39270, 43890, 46410, 51870, 53130, 62790, 66990, 67830, 71610, 79170, 82110, 84630, 85470, 91770, 94710, 99330, 101010, 103530, 108570, 111930, 117390, 122430, 128310, 136290, 140910, 144690, 154770, 161070, 164010, 166530, 168630, 182490, 191730

Offset: 1

Author

Amiram Eldar, Apr 22 2017

Keywords

• nonn

Comments

Unitary 3-abundant numbers, correspond to 3-abundant numbers (A023197).

Similarly, the first numbers k such that usigma(k) >= 4*k are 200560490130, 7420738134810, 8222980095330, and 8624101075590. - Giovanni Resta, Apr 23 2017

The least odd term in this sequence is A070826(17) = 961380175077106319535 and the least odd number k such that usigma(k) >= 4*k is A070826(52) = 5.312...*10^95. - Amiram Eldar, Dec 26 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A034448, A023197, A034683, A070826.

Programs

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; Select[Range[100000], usigma[#] >= 3*# &]

PARI

isok(k) = sumdivmult(k, d, if(gcd(d, k/d)==1, d)) >= 3*k; \\ Michel Marcus, Dec 26 2020