A104900 Numbers n such that sigma(n) = 6*phi(n).

6, 70, 616, 1240, 2090, 8932, 17980, 19780, 20320, 26980, 29512, 43180, 49742, 51688, 58058, 79000, 100130, 116870, 128570, 175370, 176715, 201376, 208280, 221536, 275770, 280670, 282680, 302176, 373065, 427924, 435435, 470764, 483616, 618772, 642124

Offset: 1

Author

Farideh Firoozbakht, Apr 01 2005

Keywords

• nonn

Comments

If p>2 & 2^p-1 is prime (a Mersenne prime) then 5*2^(p-2)*(2^p-1) is in the sequence. So 5*2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence.

Examples

			p>2, q=2^p-1(q is prime); m=5*2^(p-2)*q so sigma(m)=6*(2^(p-1)-1)*2^p=6*phi(m) hence m is in the sequence.
sigma(79000)=187200=6*31200 =6*phi(79000) so 79000 is in the sequence but 79000 is not of the form 5*2^(p-2)*(2^p-1).
		

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. A000043, A062699, A068390, A104901.

Programs

Mathematica

Do[If[DivisorSigma[1, m] == 6*EulerPhi[m], Print[m]], {m, 1000000}]

PARI

is(n)=sigma(n)==6*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013

PARI

v=List(); forfactored(n=6,10^6, if(sigma(n)==6*eulerphi(n), listput(v,n[1]))); Vec(v) \\ Charles R Greathouse IV, May 09 2017