A068391 Numbers n such that sigma(n) = 3*phi(n).

2, 15, 357, 3339, 5049, 10659, 12441, 24969, 99693, 124355, 132957, 145145, 353133, 423657, 596037, 655707, 734517, 745503, 894387, 1406427, 1641783, 1823877, 1936557, 3295047, 4108401, 4194183, 4776201, 5574699, 5842137, 5971251, 6132789, 6953765, 7649915

Offset: 1

Author

Benoit Cloitre, Mar 03 2002

Keywords

• easy
• nonn

Comments

From Farideh Firoozbakht, May 01 2009: (Start)

If m>1 and 2*3^m-1 is prime then n = 7*3^(m-1)*(2*3^m-1) is in the sequence.

Because sigma(n) = 8*(3^m-1)/2*(2*3^m) = 8*3^m*(3^m-1) = 3*6*(2*3^(m-2))*(2*3^m-2) = 3*phi(7)*phi(3^(m-1))*phi(2*3^m-1) = 3*phi(7*3^(m-1)*(2*3^m-1)) = 3*phi(n). (End)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie, terms 1..1000 from Donovan Johnson)
• Kevin A. Broughan and Daniel Delbourgo, On the Ratio of the Sum of Divisors and Euler’s Totient Function I, Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8.
• Kevin A. Broughan and Qizhi Zhou, On the Ratio of the Sum of Divisors and Euler's Totient Function II, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.2.

Crossrefs

Cf. A000203.

Subsequence of A087943 (sigma(k) is a multiple of 3).

Programs

Mathematica

Select[Range[765*10^4],DivisorSigma[1,#]==3EulerPhi[#]&] (* Harvey P. Dale, Aug 25 2019 *)

PARI

for(n=1,500000, if(sigma(n)==3*eulerphi(n),print1(n,",")))

Extensions

More terms from Rick L. Shepherd, May 14 2002