# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a105261 Showing 1-1 of 1 %I A105261 #16 Sep 23 2020 04:39:48 %S A105261 1,8,108,250,6174,41154 %N 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). %C A105261 This sequence has exactly six terms (see the Monthly reference). phi(n)=A000010(n); c(n)=A007947(n). %D A105261 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 108, p. 38, Ellipses, Paris 2008. %D A105261 J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 745 ; pp 95; 317-8, Ellipses Paris 2004. %D A105261 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 A105261 J.-M. De Koninck, When the Totient Is the Product of the Squared Prime Divisors: Problem 10966, Amer. Math. Monthly, 111 (2004), p. 536. %e A105261 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 A105261 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 A105261 Select[Range[42000], EulerPhi[#] == Times @@ FactorInteger[#][[All,1]]^2 & ] (* _Jean-François Alcover_, Sep 12 2011 *) %Y A105261 Cf. A000010, A007947. %K A105261 fini,nonn,full %O A105261 1,2 %A A105261 _Emeric Deutsch_, Apr 14 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE