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 A068390 Numbers n such that sigma(n) = 4*phi(n). 20
 14, 105, 248, 418, 1485, 3135, 3596, 3956, 4064, 5396, 8636, 20026, 23374, 25714, 35074, 35343, 39105, 41656, 55154, 56134, 56536, 71145, 74613, 87087, 124605, 150195, 175305, 192855, 263055, 393104, 413655, 421005, 474548, 604012, 697851, 711988, 819772 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If 2^p-1 is a prime (Mersenne prime) greater than 3 then (2^(p-2)*(2^p-1) is in the sequence. So for n>1, 2^(A000043(n)-2)*(2^A000043(n)-1) is in the sequence. - Farideh Firoozbakht, Feb 23 2005 Theorem: If m>0, k is integer and p=2^(m+2)+k-1 is a prime number then n=2^m*p is a solution to the equation sigma(x) = 4*phi(x)-k. The previous comment is the special case k=0. - Farideh Firoozbakht, Oct 01 2014 REFERENCES D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 88. 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. F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1 MATHEMATICA Select[Range[900000], DivisorSigma[1, #]==4EulerPhi[#]&] (* Harvey P. Dale, Nov 29 2013 *) PROG (PARI) for(n=1, 300000, if(sigma(n)==4*eulerphi(n), print1(n, ", "))) (Magma) [n: n in [1..10^6] | SumOfDivisors(n) eq 4*EulerPhi(n)]; // Vincenzo Librandi, Sep 25 2017 CROSSREFS Cf. A000010, A000203, A079546, A000043, A292422. Subsequence of A248150 (sigma(k) is divisible by 4). Sequence in context: A222369 A131709 A139614 * A162632 A220893 A008506 Adjacent sequences: A068387 A068388 A068389 * A068391 A068392 A068393 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Mar 03 2002 EXTENSIONS More terms from Carl Najafi, Aug 16 2011 STATUS approved

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Last modified August 3 23:57 EDT 2024. Contains 374905 sequences. (Running on oeis4.)