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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

Adjacent sequences:  A068388 A068389 A068390 * A068392 A068393 A068394

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 February 19 13:20 EST 2020. Contains 332044 sequences. (Running on oeis4.)