A163667 Numbers n such that sigma(n) = 9*phi(n).

30, 264, 714, 3080, 3828, 6678, 10098, 12648, 21318, 22152, 24882, 44660, 49938, 61344, 86304, 94944, 118296, 129504, 130356, 147560, 183396, 199386, 201756, 207264, 216936, 248710, 258440, 265914, 275196, 290290, 321204, 505164, 628776, 706266, 706836

Offset

1,1

Comments

This sequence is a subsequence of A011257 because sqrt(phi(n)*sigma(n)) = 3*phi(n).

If 2^p-1 and 2*3^k-1 are two primes greater than 5 then n = 2^(p-2)*(2^p-1)*3^(k-1)*(2*3^k-1) (the product of two relatively prime terms 2^(p-2)*(2^p-1) and 3^(k-1)*(2*3^k-1) of A011257) 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.

Mathematica

Select[Range[700000], DivisorSigma[1, # ]==9EulerPhi[ # ]&]

Prog

(PARI) is(n)=sigma(n)==9*eulerphi(n) \\ Charles R Greathouse IV, May 09 2013

Crossrefs

Cf. A000010, A000043, A000203, A000668, A003307, A011257, A079363.

Sequence in context: A230615 A230731 A053358 * A214944 A259455 A270852

Adjacent sequences: A163664 A163665 A163666 * A163668 A163669 A163670

Keyword

easy,nonn

Author

M. F. Hasler and Farideh Firoozbakht, Aug 09 2009

Status

approved