A063752 - OEIS
1, 2, 3, 5, 6, 7, 8, 11, 13, 17, 19, 21, 23, 24, 27, 28, 29, 31, 32, 37, 41, 43, 47, 53, 54, 59, 61, 67, 68, 69, 71, 73, 79, 83, 89, 96, 97, 101, 103, 107, 109, 112, 113, 124, 125, 127, 128, 131, 133, 137, 139, 141, 149, 151, 157, 163, 167, 173, 179, 181, 189, 191
COMMENTS
Some different families and subsequences of integers belong to this sequence, see the file "Subfamilies and subsequences" for more details, with data, comments, proofs, formulas and examples. - Bernard Schott, Mar 05 2019
LINKS
Thomas E. Moore, Problem 1204, Crux Mathematicorum, page 93, Vol. 14, Mar. 88.
FORMULA
a(n) seems to be asymptotic to c * n * log(n) with c = 1.7... (all primes are in the sequence since cototient(p) = 1). - Benoit Cloitre, Sep 08 2002
MATHEMATICA
Select[Range[200], IntegerQ[Sqrt[# - EulerPhi[#]]]&] (* Jean-François Alcover, Nov 06 2016 *)
PROG
(PARI) j=[]; for(n=1, 400, x=n-eulerphi(n); if(issquare(x), j=concat(j, n))); j
(PARI) { n=0; for (m=1, 10^9, if (issquare(m - eulerphi(m)), write("b063752.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 29 2009
(Magma) [n: n in [1..200] | IsSquare(n - EulerPhi(n))]; // Vincenzo Librandi, Jan 11 2019