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 A105261 Values of n such that phi(n)=c(n)^2, where phi is the Euler totient function and c(n) is the product of the distinct prime factors of n (c(1)=1). 1
 1, 8, 108, 250, 6174, 41154 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence has exactly six terms (see the Monthly reference). phi(n)=A000010(n); c(n)=A007947(n). REFERENCES J.-M. De Konick, Problem 10966, Amer. Math. Monthly, 111 (2004), p. 536. J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 108, p. 38, Ellipses, Paris 2008. J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 745 ; pp 95; 317-8, Ellipses Paris 2004. J.-M. De Koninck & A. Mercier, 1001 Problems in Classical Number Theory, Problem 745 ; pp 80; 273-4, Amer. Math. Soc. Providence RI 2007. LINKS EXAMPLE 8 is in the sequence because phi(8)=4 (1,3,5,7), c(8)=2 (2 being the only prime divisor of 8) and so phi(8)=c(8)^2. MAPLE with(numtheory): c:=proc(n) local div: div:=convert(factorset(n), list): product(div[j], j=1..nops(div)) end:p:=proc(n) if phi(n)=c(n)^2 then n else fi end: seq(p(n), n=1..42000); MATHEMATICA Select[Range[42000], EulerPhi[#] == Times @@ FactorInteger[#][[All, 1]]^2 & ] (* From Jean-François Alcover, Sep 12 2011 *) CROSSREFS Cf. A000010, A007947. Sequence in context: A000845 A199658 A027013 * A187288 A187190 A099762 Adjacent sequences:  A105258 A105259 A105260 * A105262 A105263 A105264 KEYWORD fini,nonn,full AUTHOR Emeric Deutsch, Apr 14 2005 STATUS approved

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Last modified May 26 02:31 EDT 2013. Contains 225652 sequences.