A136540 Numbers n such that sigma(n) = 7*phi(n).

12, 78, 140, 910, 2214, 4180, 4674, 8008, 16120, 25758, 27170, 46816, 54530, 58302, 94240, 99484, 116116, 200260, 233740, 257140, 264160, 350740, 371898, 383656, 479864, 518022, 523218, 551540, 561340, 575598, 616722, 646646, 785118, 965960, 1027000

Offset

1,1

Comments

If 2^p-1 is a Mersenne prime greater than 3 then m = 65*2^(p-2)*(2^p-1) is in the sequence (the proof is easy).

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(12) = 28 = 7*phi(12) so 12 is in the sequence.

Maple

with(numtheory): A136540:=n->`if`(sigma(n)=7*phi(n), n, NULL): seq(A136540(n), n=1..10^5); # Wesley Ivan Hurt, Feb 11 2017

Mathematica

Do[If[DivisorSigma[1, n]==7*EulerPhi[n], Print[n]], {n, 600000}]
(* Second program *)
Select[Range[10^6], DivisorSigma[1, #] == 7 EulerPhi@ # &] (* Michael De Vlieger, Feb 12 2017 *)

Prog

(PARI) is(n)=sigma(n)==7*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013

Crossrefs

Cf. A000043, A000668, A068390, A104900, A104901, A104902, A104903.

Sequence in context: A210695 A109711 A244390 * A139612 A304503 A268793

Adjacent sequences: A136537 A136538 A136539 * A136541 A136542 A136543

Keyword

easy,nonn

Author

Farideh Firoozbakht, Jan 05 2008

Status

approved