OFFSET
1,2
COMMENTS
Also numbers n such that n = y*phi(y) for a unique positive integer y (see A194507). - Franz Vrabec, Aug 27 2011
Sequence A002618 sorted into ascending order; also A327171 sorted into ascending order, with duplicate terms removed. Indices of nonzero terms in A327170 and in A327172. - Antti Karttunen, Sep 29 2019
REFERENCES
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 3, p. 224.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)
Walther Janous, Problem 6588, Advanced Problems, The American Mathematical Monthly, Vol. 95, No. 10 (1988), p. 963; How Often is n*phi(n) <= x^2?, Solution to Problem 6588, ibid., Vol. 98, No. 5 (1991), pp. 446-448.
FORMULA
From Antti Karttunen, Sep 29 2019: (Start)
(End)
The number of terms not exceeding x is ~ c * sqrt(x), where c = Product_{p prime} (1 + 1/sqrt(p*(p-1)) - 1/p) = 1.3651304521... (Janous, 1988). - Amiram Eldar, Mar 10 2021
MATHEMATICA
With[{nn = 1700}, TakeWhile[Union@ Array[EulerPhi[#] (Sqrt@ # /. (c_: 1) a_^(b_: 0) :> (c a^b)^2) &, nn], # <= nn &]] (* Michael De Vlieger, Sep 29 2019, after Bill Gosper at A007913 *)
PROG
(PARI) isok(n) = {for (x=1, n, if (eulerphi(x)*core(x) == n, return (1)); ); return (0); } \\ Michel Marcus, Dec 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 27 2003
STATUS
approved