A289126 Numbers n such that usigma(usigma(n))/usigma(n) > usigma(usigma(m))/usigma(m) for all m < n, where usigma(n) is the sum of unitary divisors of n (A034448).

1, 2, 5, 18, 164, 1538, 20018, 408404, 7759748, 148728578, 6976017044, 7317446132

Offset: 1

Author

Amiram Eldar, Jun 25 2017

Keywords

• nonn
• more

Comments

The unitary version of A289124.

Links

• Paul Erdős and M. V. Subbarao, On the iterates of some arithmetic functions, The theory of arithmetic functions (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich. 1971), Lecture Notes in Math., 251 , pp. 119-125, Springer, Berlin, 1972. [alternate link]

Crossrefs

Cf. A034448, A055033, A289124.

Programs

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; a = {}; k=1; rmax = 0; While[Length[a]<8, s = usigma[ k]; s2 = usigma[ s]; r = s2/s;  If[r > rmax, AppendTo[a, k]; rmax = r]; k++]; a

Extensions

a(10)-a(12) from Giovanni Resta, Aug 23 2017