A001229 Numbers n such that phi(sigma(n)) = n.

1, 2, 8, 12, 128, 240, 720, 6912, 32768, 142560, 712800, 1140480, 1190400, 3345408, 3571200, 5702400, 14859936, 29719872, 50319360, 118879488, 2147483648, 3889036800, 4389396480, 21946982400, 47416320000, 92177326080, 133145026560, 331914240000

Offset

1,2

Comments

For n=0,1,2,3,4 & 5 2^(2^n-1) is in the sequence because 2^2^n+1 is prime for n=0,1,2,3 & 4 (Fermat primes). - Farideh Firoozbakht, Oct 08 2004

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 128, p. 44, Ellipses, Paris 2008.

J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 702 pp. 92; 300-1, Ellipses Paris 2004.

R. K. Guy, Unsolved Problems in Number Theory, B42.

Links

Table of n, a(n) for n=1..28.

Leon Alaoglu and Paul Erdős, A conjecture in elementary number theory, Bull. Amer. Math. Soc. 50 (1944), pp. 881-882.

Graeme L. Cohen, On a conjecture of Makowski and Schinzel, Colloquium Mathematicae, Vol. 74, No. 1 (1997), pp. 1-8. See Notes p. 7.

Fred W. Helenius, 664 solutions [Broken Link]

Fred W. Helenius, 664 solutions [From the Wayback machine]

T. Negadi, The genetic code invariance: when Euler and Fibonacci meet, arXiv preprint arXiv:1406.6092 [q-bio.OT], 2014; Symmetry: Culture and Science, Vol. 25, No. 3, 261-278, 2014.

Eric Weisstein's World of Mathematics, Totient Function.

Formula

phi(A018784), sorted. - David W. Wilson, Oct 18 2012

Mathematica

Select[Range[10000], EulerPhi[DivisorSigma[1, #]] == # &] (* T. D. Noe, Jun 26 2012 *)

Prog

(PARI) is(n)=eulerphi(sigma(n))==n \\ Charles R Greathouse IV, May 15 2013

Crossrefs

Cf. A000010, A018784, A135240.

Sequence in context: A331459 A330816 A066471 * A298640 A120000 A067678

Adjacent sequences: A001226 A001227 A001228 * A001230 A001231 A001232

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson, Aug 15 1996 (search was complete only through a(19) = 50319360).

Jud McCranie reports Jun 15 1998 that the terms through a(24) are certain.

a(28) added. Verified sequence is complete through a(28) by Donovan Johnson, Jun 30 2012

Status

approved