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A063752 Numbers k such that cototient(k) is a square. 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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
CROSSREFS
Sequence in context: A123030 A284836 A267300 * A191893 A016741 A191167
KEYWORD
nonn
AUTHOR
Jason Earls, Aug 11 2001
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)