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 A058277 Number of values of k such that phi(k) = n, where n runs through the values (A002202) taken by phi. 21
 2, 3, 4, 4, 5, 2, 6, 6, 4, 5, 2, 10, 2, 2, 7, 8, 9, 4, 3, 2, 11, 2, 2, 3, 2, 9, 8, 2, 2, 17, 2, 10, 2, 6, 6, 3, 17, 4, 2, 3, 2, 9, 2, 6, 3, 17, 2, 9, 2, 7, 2, 2, 3, 21, 2, 2, 7, 12, 4, 3, 2, 12, 2, 8, 2, 10, 4, 2, 21, 2, 2, 8, 3, 4, 2, 3, 19, 5, 2, 8, 2, 2, 6, 2, 31, 2, 9, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Carmichael (1922) conjectured that the number 1 never appears in this sequence. Sierpiński conjectured and Ford (1998) proved that all integers greater than 1 occur in the sequence. Erdős (1958) proved that if s >= 1 appears in the sequence then it appears infinitely often. - Nick Hobson, Nov 04 2006 A002202(n) occurs a(n) times in A007614. - Reinhard Zumkeller, Nov 22 2015 REFERENCES E. Lucas, Théorie des Nombres, Blanchard 1958. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 R. D. Carmichael, Note on Euler's totient function, Bull. Amer. Math. Soc. 28 (1922), pp. 109-110. P. Erdős, Some remarks on Euler's totient function, Acta Arith. 4 (1958), pp. 10-19. K. Ford, The distribution of totients, Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 27-34. N. Hobson, Problem 152, "Totient valence" Eric Weisstein's World of Mathematics, Totient Valence Function MATHEMATICA max = 300; inversePhi[_?OddQ] = {}; inversePhi[1] = {1, 2}; inversePhi[m_] := Module[{p, nmax, n, nn}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m * Times @@ (p/(p-1)); n = m; nn = Reap[While[n <= nmax, If[EulerPhi[n] == m, Sow[n]]; n++]] // Last; If[nn == {}, {}, First[nn] ] ]; Reap[For[n = 1, n <= max, n = If[n == 1, 2, n+2], nn = inversePhi[n] ; If[nn != {} , Sow[nn // Length] ] ] ] // Last // First (* Jean-François Alcover, Nov 21 2013 *) PROG (Haskell) import Data.List (group) a058277 n = a058277_list !! (n-1) a058277_list = map length \$ group a007614_list -- Reinhard Zumkeller, Nov 22 2015 CROSSREFS The nonzero terms of A014197. Cf. A000010, A002202. Cf. A007614. Sequence in context: A211509 A305594 A320778 * A065852 A303998 A319712 Adjacent sequences:  A058274 A058275 A058276 * A058278 A058279 A058280 KEYWORD nonn,easy AUTHOR Claude Lenormand (claude.lenormand(AT)free.fr), Jan 05 2001 EXTENSIONS More terms from Nick Hobson, Nov 04 2006 STATUS approved

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Last modified February 20 19:41 EST 2020. Contains 332084 sequences. (Running on oeis4.)