A063755 - OEIS

%I #30 Aug 18 2024 15:24:43

%S 1,4,16,36,64,144,256,324,576,1024,1296,2304,2916,4096,5184,9216,

%T 11664,16384,20736,26244,36864,46656,65536,82944,104976,147456,186624,

%U 236196,262144,331776,419904,589824,746496,944784,1048576,1327104

%N Squares k which are divisible by phi(k).

%H Amiram Eldar, <a href="/A063755/b063755.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..160 from Harry J. Smith)

%F From _Amiram Eldar_, Oct 29 2020: (Start)

%F a(n) = A007694(n)^2.

%F Sum_{n>=1} 1/a(n) = 11/8. (End)

%t Select[ Range[ 1, 2000 ], Mod[ #^2, EulerPhi[ #^2 ] ]==0& ]^2

%t Select[Range[2000]^2,Divisible[#,EulerPhi[#]]&] (* _Harvey P. Dale_, Dec 11 2010 *)

%t Join[{1}, Sort @ Flatten @ Table[2^i*3^j, {i, 2, Log2[m], 2}, {j, 0, Log[3, m/2^i], 2}]] (* _Amiram Eldar_, Oct 29 2020 *)

%o (PARI) j=[]; for(n=1,2000, if(Mod(n^2,eulerphi(n^2))==0,j=concat(j,n^2))); j

%o (PARI) { n=0; for (m=1, 10^9, s=m^2; if (s%eulerphi(s)==0, write("b063755.txt", n++, " ", s); if (n==160, break)) ) } \\ _Harry J. Smith_, Aug 29 2009

%Y Cf. A000010, A000290, A049237, A007694. Squares arising in A007694.

%K nonn

%O 1,2

%A _Jason Earls_, Aug 14 2001

%E More terms from _Dean Hickerson_, Aug 15 2001