A104902 Numbers n such that sigma(n) = 12*phi(n).

210, 1848, 2970, 3720, 6270, 26796, 38340, 53940, 59340, 60960, 70686, 78210, 80940, 88536, 129540, 142290, 149226, 155064, 174174, 237000, 249210, 300390, 350610, 385710, 429408, 526110, 604128, 624840, 664608, 827310, 828072, 842010, 848040, 906528

Offset

1,1

Comments

If p>2 and 2^p-1 is prime (a Mersenne prime) then 15*2^(p-2)*(2^p-1) is in the sequence. So 15*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=15*2^(p-2)*q so sigma(m)=24*(2^(p-1)-1)*2^p=12*(8*2^(p-3)*(2^p-2))=12*phi(m) hence m is in the sequence.
sigma(237000)=748800=12*62400=12*phi(237000) so 237000 is in the sequence but 237000 is not of the form 15*2^(p-2)*(2^p-1).

Mathematica

Do[If[DivisorSigma[1, m] == 12*EulerPhi[m], Print[m]], {m, 1200000}]

Prog

(PARI) is(n)=sigma(n)==12*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013

Crossrefs

Cf. A000043, A062699, A068390, A104900, A104901.

Sequence in context: A047633 A187317 A187309 * A371111 A371053 A135201

Adjacent sequences: A104899 A104900 A104901 * A104903 A104904 A104905

Keyword

easy,nonn

Author

Farideh Firoozbakht, Apr 01 2005

Status

approved