A069823 Nonprime numbers k such there is no x < k such that phi(x) = phi(k).

1, 15, 25, 35, 51, 65, 69, 81, 85, 87, 121, 123, 129, 141, 143, 159, 161, 177, 185, 187, 203, 213, 235, 247, 249, 253, 255, 265, 267, 275, 289, 299, 301, 309, 321, 323, 339, 341, 343, 361, 393, 403, 415, 425, 447, 485, 489, 501, 519, 527, 529, 535, 537, 551

Offset

1,2

Comments

If p is prime there is no x < p such that phi(x) = phi(p) = p-1 since phi(x) < p-1.

Nonprime numbers n such that A081373(n)=1; i.e., number of numbers not exceeding n and with identical value of their phi than that of n, equals one. - Labos Elemer, Mar 24 2003

For 1 < n, if a(n) is squarefree, then phi(a(n)) is nonsquarefree. The converse is also true. For 1 < n, if phi(a(n)) is squarefree then a(n) is nonsquarefree. - Torlach Rush, Dec 26 2017

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

k=25, a nonprime; phi values for k <= 25 are {1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8,12,10,22,8,20}; no phi(k) except phi(25) equals 20, A081373(25)=1; if n is prime then A081373(n)=1 holds.

Mathematica

f[x_] := EulerPhi[x] fc[x_] := Count[Table[f[j]-f[x], {j, 1, x}], 0] t1=Flatten[Position[Table[fc[w], {w, 1, 1000}], 1]] t2=Flatten[Position[PrimeQ[t1], False]] Part[t1, t2]
(* Second program: *)
Union@ Select[Values[PositionIndex@ Array[EulerPhi, 600]][[All, 1]], ! PrimeQ@ # &] (* Michael De Vlieger, Dec 31 2017 *)

Prog

(PARI) for(s=2, 600, if((1-isprime(s))*abs(prod(i=1, s-1, eulerphi(i)-eulerphi(s)))>0, print1(s, ", ")))

Crossrefs

Cf. A081373, A067004, A000010.

Sequence in context: A349750 A171133 A152246 * A133321 A031888 A299469

Adjacent sequences: A069820 A069821 A069822 * A069824 A069825 A069826

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 28 2002

Status

approved