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

1,1

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.

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.

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A000043, A062699, A068390, A104901.

Sequence in context: A188406 A048708 A286527 * A186667 A001448 A024489

Adjacent sequences: A104897 A104898 A104899 * A104901 A104902 A104903

Keyword

nonn

Author

Farideh Firoozbakht, Apr 01 2005

Status

approved