A289124 Numbers n such that sigma(sigma(n))/sigma(n) > sigma(sigma(m))/sigma(m) for all m < n.

1, 2, 3, 5, 6, 14, 22, 24, 54, 88, 114, 120, 264, 312, 520, 540, 864, 1560, 3432, 4320, 8856, 9120, 10464, 20664, 21276, 32760, 36840, 52320, 92280, 106380, 170040, 185760, 201240, 417960, 613080, 1059480, 1098720, 1937880, 2213640, 2982240, 5611320, 9809280

Offset: 1

Author

Amiram Eldar, Jun 25 2017

Keywords

• nonn

Comments

Erdős proved that sigma(sigma(n))/sigma(n) is unbounded, thus this sequence is infinite.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..61
• Paul Erdős, Some remarks on the iterates of the phi and sigma functions, Colloquium Mathematicae, Vol. 17, No. 2 (1967), pp. 195-202.

Crossrefs

Cf. A000203, A051027, A066961.

Programs

Mathematica

a = {}; k=1; rmax = 0; While[Length[a]<40,s = DivisorSigma[1, k]; s2 = DivisorSigma[1, s]; r = s2/s; If[r > rmax, AppendTo[a, k]; rmax = r]; k++]; a

PARI

r=0; forfactored(n=1,10^10, t=sigma(sigma(n),-1); if(t>r, r=t; print1(n[1]", "))) \\ Charles R Greathouse IV, Jun 25 2017