A286268 Totient superabundant numbers: numbers n such that A092693(n)/n > A092693(m)/m for all m < n.

1, 2, 3, 5, 11, 17, 83, 137, 257, 2879, 46049, 65537

Offset: 1

Author

Amiram Eldar, May 05 2017

Keywords

• nonn
• more

Comments

Analogous to A004394 (superabundant numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).

The first 6 terms of A092506 (primes of the form 2^n + 1) are in this sequence.

a(13) > 1.6*10^10, if it exists. - Giovanni Resta, May 05 2017

Links

• Paul Loomis and Florian Luca, On totient abundant numbers, Electronic Journal of Combinatorial Number Theory, Vol. 8, #A06 (2008).

Crossrefs

Cf. A000396, A004394, A082897, A092506, A092693, A286265, A286267.

Programs

Mathematica

Function[s, Flatten[First@ Position[s, #] & /@ Union@ Rest@ FoldList[Max, 0, s]]]@ Table[(Total@ FixedPointList[EulerPhi, n] - (n + 1))/n, {n, 10^5}] (* Michael De Vlieger, May 06 2017, after Alonso del Arte at A092693 *)