A286267 -id:A286267 - cp's OEIS frontend

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

Amiram Eldar, May 05 2017

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

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

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

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 *)

A286322 Totient highly abundant numbers that are composite.

Original entry on oeis.org

4, 9, 221, 289, 697, 1819, 2329, 4369, 4913, 6439, 18769, 21331, 35209, 66049, 128881, 184783, 197143, 258121, 281929, 516961, 739903, 971203, 1762249, 1942663, 2070721, 2898703, 2952673, 3820819, 4142881, 5550943, 5869681, 8288641, 16230481, 16773619

Offset: 1

Amiram Eldar, May 07 2017

nonn

Intersection of A002808 and A286267.

Of the 65 terms below 10^9, only 2 have more than 2 prime factors: a(9) = 17^3 and a(36) = 257^3, and 11 are prime powers: a(1) = 2^2, a(2) = 3^2, a(4) = 17^2, a(9) = 17^3, a(11) = 137^2, a(14) = 257^2, a(15) = 359^2, a(20) = 719^2, a(25) = 1439^2, a(32) = 2879^2, and a(36) = 257^3.

Amiram Eldar and Giovanni Resta, Table of n, a(n) for n = 1..93 (terms < 5*10^10, first 65 terms from Amiram Eldar)

Cf. A002808, A286267.

sumTot[n_] := Plus @@ FixedPointList[ EulerPhi@ # &, n] - 1; a={};smax=0;For[k=1,k<300000,k++;s=sumTot[k];If[s>smax,smax=s;If[!PrimeQ[k],a=AppendTo[a,k]]]];a

cp's OEIS Frontend

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

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