A066694 Numbers k such that phi(sigma(k)) > k.

4, 9, 16, 18, 25, 32, 36, 48, 50, 64, 72, 81, 84, 98, 100, 112, 144, 156, 162, 192, 196, 200, 225, 252, 256, 288, 289, 300, 324, 336, 338, 372, 392, 400, 432, 448, 450, 468, 484, 512, 576, 578, 624, 625, 648, 676, 700, 722, 729, 756, 768, 784, 800, 882, 900

Offset: 1

Author

Joseph L. Pe, Jan 09 2002

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Amiram Eldar, Plot of a(n)/(n*log(n)^2) for n = 2^(4..21).

Crossrefs

Cf. A000010, A000203, A001229, A062401, A295307.

Programs

Mathematica

Select[Range[1, 10^3], EulerPhi[DivisorSigma[1, # ]] > # &]

PARI

{ n=0; for (m=1, 10^10, if (eulerphi(sigma(m)) > m, write("b066694.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 18 2010

Formula

It seems that a(n) is asymptotic to C*n*log(n)^2 with C=1.38.... - Benoit Cloitre, Aug 07 2002

Extensions

More terms from Benoit Cloitre, Jul 31 2002