A066993 Integer of the form phi(n)*sigma(n)/n.

1, 4, 13, 20, 24, 36, 40, 65, 64, 84, 112, 96, 128, 121, 171, 186, 200, 216, 168, 208, 192, 273, 312, 340, 392, 364, 480, 448, 456, 496, 612, 605, 576, 640, 768, 768, 840, 880, 840, 936, 960, 1105, 992, 1200, 1093, 1280, 1464, 1364, 1152, 1539, 1152, 1664, 1482

Offset: 1

Author

Benoit Cloitre, Jan 27 2002

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A011775.

Programs

Mathematica

Select[Table[EulerPhi[n] DivisorSigma[1,n]/n,{n,2000}],IntegerQ] (* Harvey P. Dale, Mar 17 2020 *)

PARI

{ n=0; for (m=1, 10^10, if ((a=eulerphi(m)*sigma(m)/m) % 1.0 == 0 , write("b066993.txt", n++, " ", a); if (n==1000, return)) ) } \\ Harry J. Smith, Apr 16 2010

Formula

a(n) = sigma(A011775(n))*phi(A011775(n))/A011775(n).

Extensions

Missing term a(43)=992 and new term a(53)=1482 added by Harry J. Smith, Apr 16 2010