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A068391 Numbers n such that sigma(n) = 3*phi(n). 7
2, 15, 357, 3339, 5049, 10659, 12441, 24969, 99693, 124355, 132957, 145145, 353133, 423657, 596037, 655707, 734517, 745503, 894387, 1406427, 1641783, 1823877, 1936557, 3295047, 4108401, 4194183, 4776201, 5574699, 5842137, 5971251, 6132789, 6953765, 7649915 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Farideh Firoozbakht, May 01 2009: (Start)
If m>1 and 2*3^m-1 is prime then n=7*3^(m-1)*(2*3^m-1) is in the sequence.
Because sigma(n)=8*(3^m-1)/2*(2*3^m)=8*3^m*(3^m-1)=3*6*(2*3^(m-2))*(2*3^m-2) =3*phi(7)*phi(3^(m-1))*phi(2*3^m-1))=3*phi(7*3^(m-1)*(2*3^m-1))=3*phi(n). (End)
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[765*10^4], DivisorSigma[1, #]==3EulerPhi[#]&] (* Harvey P. Dale, Aug 25 2019 *)
PROG
(PARI) for(n=1, 500000, if(sigma(n)==3*eulerphi(n), print1(n, ", ")))
CROSSREFS
Cf. A000203.
Subsequence of A087943 (sigma(k) is a multiple of 3).
Sequence in context: A297077 A175563 A231443 * A215743 A254224 A071102
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 03 2002
EXTENSIONS
More terms from Rick L. Shepherd, May 14 2002
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)