A068390 Numbers n such that sigma(n) = 4*phi(n).

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

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