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A105261
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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).
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1
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OFFSET
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1,2
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COMMENTS
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This sequence has exactly six terms (see the Monthly reference). phi(n)=A000010(n); c(n)=A007947(n).
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..6.
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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Select[Range[42000], EulerPhi[#] == Times @@ FactorInteger[#][[All, 1]]^2 & ] (* From Jean-François Alcover, Sep 12 2011 *)
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CROSSREFS
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Cf. A000010, A007947.
Sequence in context: A000845 A199658 A027013 * A187288 A187190 A099762
Adjacent sequences: A105258 A105259 A105260 * A105262 A105263 A105264
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KEYWORD
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fini,nonn,full
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AUTHOR
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Emeric Deutsch, Apr 14 2005
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STATUS
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approved
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