The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A006517 Numbers k such that k divides 2^k + 2. (Formerly M1719) 20
 1, 2, 6, 66, 946, 8646, 180246, 199606, 265826, 383846, 1234806, 3757426, 9880278, 14304466, 23612226, 27052806, 43091686, 63265474, 66154726, 69410706, 81517766, 106047766, 129773526, 130520566, 149497986, 184416166, 279383126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All terms greater than 1 are even. If an odd term n>1 exists then n = m*2^k + 1 for some k>=1 and odd m. Then n divides 2^(m*2^k) + 1 and so does every prime factor p of n, implying that 2^(k+1) divides the multiplicative order of 2 modulo p and thus p-1. Therefore n = m*2^k + 1 is the product of prime factors of the form t*2^(k+1) + 1, implying that n-1 is divisible by 2^(k+1), a contradiction. - Max Alekseyev, Mar 16 2009 The sequence is infinite. In fact, its intersection with A055685 (given by A219037) is infinite (see Li et al. link). - Max Alekseyev, Oct 11 2012 All terms greater than 6 have at least three distinct prime factors. - Robert Israel, Aug 21 2014 REFERENCES R. Honsberger, Mathematical Gems, M.A.A., 1973, p. 142. Sierpiński, W. 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970. Problem #18 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Giovanni Resta, Table of n, a(n) for n = 1..150 Kin Y. Li et al., Solution to Problem 323, Mathematical Excalibur 14(2), 2009, p. 3. V. Meally, Letter to N. J. A. Sloane, May 1975 MATHEMATICA Do[ If[ PowerMod[ 2, n, n ] + 2 == n, Print[n]], {n, 2, 1500000000, 4} ] Join[{1}, Select[Range[28*10^7], PowerMod[2, #, #]==#-2&]] (* Harvey P. Dale, Aug 13 2018 *) PROG (PARI) e323(n) = {for (i=1, n, if ((2^i+2) % i == 0, print1(i, ", ")); ); } \\ Michel Marcus, Oct 07 2012 (PARI) is_A006517(n)=!(Mod(2, n)^n+2)  \\ M. F. Hasler, Oct 08 2012 CROSSREFS Cf. A006521, A015888, A015889, A015891, A015892, A015893, A015897, A015898, A015902, A015903, A015904, A015905, A015906. Sequence in context: A082619 A046399 A082617 * A217630 A091458 A335934 Adjacent sequences:  A006514 A006515 A006516 * A006518 A006519 A006520 KEYWORD nonn,nice AUTHOR EXTENSIONS Corrected and extended by Joe K. Crump (joecr(AT)carolina.rr.com), Sep 12 2000 and Robert G. Wilson v, Sep 13 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 17 06:46 EDT 2021. Contains 343059 sequences. (Running on oeis4.)