A063755 Squares k which are divisible by phi(k).

1, 4, 16, 36, 64, 144, 256, 324, 576, 1024, 1296, 2304, 2916, 4096, 5184, 9216, 11664, 16384, 20736, 26244, 36864, 46656, 65536, 82944, 104976, 147456, 186624, 236196, 262144, 331776, 419904, 589824, 746496, 944784, 1048576, 1327104

Offset: 1

Author

Jason Earls, Aug 14 2001

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..160 from Harry J. Smith)

Crossrefs

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

Programs

Mathematica

Select[ Range[ 1, 2000 ], Mod[ #^2, EulerPhi[ #^2 ] ]==0& ]^2
Select[Range[2000]^2,Divisible[#,EulerPhi[#]]&] (* Harvey P. Dale, Dec 11 2010 *)
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 *)

PARI

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

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

Formula

From Amiram Eldar, Oct 29 2020: (Start)

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

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

Extensions

More terms from Dean Hickerson, Aug 15 2001