A286322 Totient highly abundant numbers that are composite.

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

Author

Amiram Eldar, May 07 2017

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

Cf. A002808, A286267.

Programs

Mathematica

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