%I #16 Sep 23 2020 04:39:48

%S 1,8,108,250,6174,41154

%N 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).

%C This sequence has exactly six terms (see the Monthly reference). phi(n)=A000010(n); c(n)=A007947(n).

%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 108, p. 38, Ellipses, Paris 2008.

%D J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 745 ; pp 95; 317-8, Ellipses Paris 2004.

%D J.-M. De Koninck & A. Mercier, 1001 Problems in Classical Number Theory, Problem 745 ; pp 80; 273-4, Amer. Math. Soc. Providence RI 2007.

%H J.-M. De Koninck, <a href="https://www.jstor.org/stable/4145084">When the Totient Is the Product of the Squared Prime Divisors: Problem 10966</a>, Amer. Math. Monthly, 111 (2004), p. 536.

%e 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.

%p 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);

%t Select[Range[42000], EulerPhi[#] == Times @@ FactorInteger[#][[All,1]]^2 & ] (* _Jean-François Alcover_, Sep 12 2011 *)

%Y Cf. A000010, A007947.

%K fini,nonn,full

%O 1,2

%A _Emeric Deutsch_, Apr 14 2005