A003275 Values of phi(k) when phi(k) = phi(k+1).
1, 2, 8, 48, 80, 96, 128, 240, 288, 480, 1008, 1200, 1296, 1440, 1728, 2592, 2592, 4800, 5600, 6480, 8640, 11040, 12480, 14976, 19008, 19200, 22464, 24320, 24576, 21120, 28416, 27840, 25920, 32000, 32768, 36000, 47520, 52992, 60480, 59904, 79200, 89280, 96768
Offset: 1
References
- Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B36, pp. 138-142.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10755 (calculated from the b-file at A001274; terms 1..2567 from T. D. Noe)
- Kathryn Miller, The equation phi(n) = phi(n+1), Unpublished M.S., ND..
- Kathryn Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000. Unpublished, 1972. [ See Review, Math. Comp., Vol. 27, p. 447-448, 1973 ].
- Kathryn Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000, Mathematics of Computation 27 (1973), 47-48. (Annotated scanned copy)
- Leo Moser, Some equations involving Euler's totient function, Amer. Math. Monthly, 56 (1949), 22-23.
- Eric Weisstein's World of Mathematics, Totient Function.
Programs
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Haskell
a003275 = a000010 . fromIntegral . a001274 -- Reinhard Zumkeller, May 20 2014
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Mathematica
Cases[Split[Table[EulerPhi[k],{k,1,50000}]],{,}][[1;;27,1]] (* Jean-François Alcover, Mar 20 2011 *) #[[1]]&/@Select[Partition[EulerPhi[Range[80000]],2,1],#[[1]]==#[[2]]&] (* Harvey P. Dale, Oct 03 2012 *) SequenceCases[EulerPhi[Range[200000]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 05 2019 *) -
PARI
lista(lim) = my(p1 = 1, p2); for(k = 2, lim, p2 = eulerphi(k); if(p1 == p2, print1(p1, ", ")); p1 = p2); \\ Amiram Eldar, Nov 27 2024
Comments