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 A051948 Numbers k such that k*sigma(k) == 2 (mod phi(k)). 1

%I

%S 2,3,4,5,6,7,11,13,17,19,22,23,29,31,37,41,43,47,53,59,61,67,71,73,79,

%T 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,

%U 179,181,191,193,197,199,211,223,227,229,233,239,241

%N Numbers k such that k*sigma(k) == 2 (mod phi(k)).

%D R. K. Guy, Unsolved Problems Number Theory, B37.

%H Chris Nash, There no other solutions besides 4, 6, 22 and the primes (<a href="http://web.archive.org/web/20081007045526/http://pages.prodigy.net/chris_nash/puzzle76.html">html</a>, <a href="http://web.archive.org/web/20081007045526/http://pages.prodigy.net/chris_nash/puzzle76.pdf">pdf</a>)

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_076.htm">Puzzle 76</a>

%H M. V. Subbarao, <a href="http://projecteuclid.org/euclid.pjm/1102912230">On two congruences for primality</a>, Pacific Journal of Mathematics, 52 (1974), 261-268. (<a href="http://www.math.ualberta.ca/~subbarao/documents/Subbarao1974.pdf">PDF</a>)

%t Join[{2,3,4,5,6},Select[Range[7,250],Mod[# *DivisorSigma[1,#], EulerPhi[#]] == 2&]] (* _Harvey P. Dale_, Oct 28 2013 *)

%o (PARI) a(n)=if(n<12,[2,3,4,5,6,7,11,13,17,19,22][n],prime(n-3)) \\ _Charles R Greathouse IV_, Aug 26 2011

%Y Cf. A002270.

%K nonn,nice,easy

%O 1,1

%A _N. J. A. Sloane_, Dec 21 1999

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Last modified July 31 22:21 EDT 2021. Contains 346377 sequences. (Running on oeis4.)