A285906 Numbers n such that sigma(n)/usigma(n) > sigma(m)/usigma(m) for all m < n, where sigma(n) is the sum of divisors of n (A000203) and usigma(n) is the sum of unitary divisors of n (A034448).

1, 4, 8, 16, 32, 64, 72, 144, 216, 288, 432, 864, 1728, 2592, 3456, 3600, 5184, 7200, 10800, 21600, 43200, 64800, 86400, 108000, 129600, 216000, 259200, 324000, 432000, 518400, 529200, 648000, 1058400, 2116800, 3175200, 4233600, 5292000, 6350400, 10584000

Offset: 1

Author

Amiram Eldar, Apr 28 2017

Keywords

• nonn

Comments

This sequence is infinite. The smallest values of n for which sigma(n)/usigma(n) > 2, 3 and 4 are a(7), a(19), and a(44).

Examples

			sigma(72)=195, usigma(72)=90, and their ratio 195/90=13/6 is higher than sigma(m)/usigma(m) for all m<72, thus 72 is in this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..56

Crossrefs

Cf. A000203, A034448.

Programs

Mathematica

usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
a={}; rmax=0; Do[r=DivisorSigma[1, n]/usigma[n]; If[r>rmax, AppendTo[a, n]; rmax=r], {n, 3000}]; a