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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).
5
1, 8, 108, 250, 6174, 41154
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 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.
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 & ] (* Jean-François Alcover, Sep 12 2011 *)
CROSSREFS
Sequence in context: A365818 A239985 A274892 * A187288 A275134 A187190
KEYWORD
fini,nonn,full
AUTHOR
Emeric Deutsch, Apr 14 2005
STATUS
approved