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

Author

Farideh Firoozbakht, Jan 29 2008, Jan 30 2008

Keywords

• nonn

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.

Examples

			sigma(56) = 120 = 5*24 = 5*phi(56) so 56 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.

Crossrefs

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

Programs

Mathematica

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

PARI

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