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

1,1

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).

Example

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

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 *)

Prog

(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

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).

Sequence in context: A143839 A114818 A190102 * A167561 A211575 A211583

Adjacent sequences: A060670 A060671 A060672 * A060674 A060675 A060676

Keyword

nonn

Author

Robert G. Wilson v, Apr 18 2001

Status

approved