A060675 Numbers k such that phi(x) = k has exactly 12 solutions.

160, 168, 352, 448, 816, 928, 972, 1024, 1176, 1848, 2464, 3040, 3808, 4152, 4440, 4512, 4736, 4944, 5104, 5152, 5160, 5304, 5952, 6408, 6656, 6672, 6784, 7648, 8384, 8704, 8904, 10432, 10528, 10624, 11000, 11008, 11456, 11776, 12048, 12416, 13024, 13032

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			160 = phi(187) = phi(205) = phi(328) = phi(352) = phi(374) = phi(400) = phi(410) = phi(440) = phi(492) = phi(528) = phi(600) = phi(660).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010.

Number of solutions: A007617 (0), A007366 (2), A007367 (3), A060667 (4), A060668 (5), A060669 (6), A060670 (7), A060671 (8), A060672 (9), A060673 (10), A060674 (11), this sequence (12).

Programs

Mathematica

a = Table[ 0, {15000} ]; Do[ p = EulerPhi[ n ]; If[ p < 15001, a[ [ p ] ]++ ], {n, 1, 60000} ]; Select[ Range[ 15000 ], a[ [ # ] ] == 12 & ]
Union[Transpose[Select[Tally[EulerPhi[Range[100000]]],#[[2]]==12&]][[1]]] (* Harvey P. Dale, Oct 05 2015 *)

PARI

is(n)=sum(i=1,n,eulerphi(i)==n)==12 \\ Charles R Greathouse IV, Mar 03 2014

PARI

is(k) = invphiNum(k) == 12 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp