A060673 Numbers k such that phi(x) = k has exactly 10 solutions.

24, 80, 180, 256, 264, 828, 1188, 1640, 1968, 2024, 2368, 2544, 2720, 2772, 2904, 3036, 3136, 3144, 3328, 3392, 3420, 4192, 4392, 4464, 4600, 5000, 5312, 5504, 5508, 5688, 5728, 5796, 5800, 6208, 6228, 6732, 6888, 7000, 7232, 7740, 7956, 8388, 8576, 9088

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			24 = phi(35) = phi(39) = phi(45) = phi(52) = phi(56) = phi(70) = phi(72) = phi(78) = phi(84) = phi(90).
		

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), this sequence (10), A060674 (11), A060675 (12).

Programs

Mathematica

a = Table[ 0, {10000} ]; Do[ p = EulerPhi[ n ]; If[ p < 10001, a[ [ p ] ]++ ], {n, 1, 35000} ]; Select[ Range[ 10000 ], a[ [ # ] ] == 10 & ]
Take[Select[Tally[EulerPhi[Range[50000]]],#[[2]]==10&][[;;,1]]//Union,50] (* Harvey P. Dale, Sep 15 2023 *)

PARI

is(n)=sum(i=1,n,eulerphi(i)==n)==10 \\ Charles R Greathouse IV, Mar 03 2014

PARI

is(k) = invphiNum(k) == 10 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp