A286267 Totient highly abundant numbers: numbers n such that A092693(n)+n > A092693(m)+m for all m < n.

1, 2, 3, 4, 5, 7, 9, 11, 13, 17, 23, 29, 37, 41, 47, 53, 59, 67, 71, 73, 79, 83, 89, 97, 101, 107, 127, 131, 137, 149, 167, 179, 221, 223, 227, 233, 251, 257, 289, 317, 347, 353, 359, 383, 389, 431, 443, 449, 461, 467, 503, 557, 563, 569, 587, 641, 677, 697

Offset: 1

Author

Amiram Eldar, May 05 2017

Keywords

• nonn

Comments

Analogous to A002093 (highly abundant numbers) as A082897 (perfect totient numbers) is analogous to A000396 (perfect numbers).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Paul Loomis and Florian Luca, On totient abundant numbers, Electronic Journal of Combinatorial Number Theory, Vol. 8, #A06 (2008).

Crossrefs

Cf. A000396, A002093, A082897, A092693, A286265.

Programs

Mathematica

Function[s, Flatten[First@ Position[s, #] & /@ Union@ Rest@ FoldList[Max, 0, s]]]@ Table[(Total@ FixedPointList[EulerPhi, n] - 1), {n, 10^3}] (* Michael De Vlieger, May 06 2017 *)