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

Author

Farideh Firoozbakht, Apr 01 2005

Keywords

• easy
• nonn

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.

Examples

			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).
		

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, A068390, A104900, A104901.

Programs

Mathematica

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

PARI

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