A136547 Numbers n such that sigma(n) = 5*phi(n).

56, 190, 812, 1672, 4522, 5278, 16065, 24244, 25070, 33915, 39585, 56252, 80104, 93496, 102856, 107156, 140296, 157586, 220616, 224536, 316274, 317205, 365638, 389732, 423045, 479655, 546592, 559845, 596666, 601312, 696514, 731962, 1123605, 1161508, 1181895

Offset

1,1

Comments

If p>2 and 2^p-1 is prime (a Mersenne prime) then 377*2^(p-2)*(2^p-1) is in the sequence (the proof is easy). So for n>1 377*2^(A000043(n)-2)*(2^A000043(n)-1) is in the 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

sigma(56) = 120 = 5*24 = 5*phi(56) so 56 is in the sequence.

Mathematica

Do[If[DivisorSigma[1, m]==5*EulerPhi[m], Print[m]], {m, 1500000}]

Prog

(PARI) is(n)=sigma(n)==5*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013

Crossrefs

Cf. A000043, A062699, A104900, A104901, A104902.

Sequence in context: A224108 A234114 A234107 * A264303 A200833 A241611

Adjacent sequences: A136544 A136545 A136546 * A136548 A136549 A136550

Keyword

nonn

Author

Farideh Firoozbakht, Jan 29 2008, Jan 30 2008

Status

approved