A060669 Numbers k such that phi(x) = k has exactly 6 solutions.

12, 16, 84, 88, 112, 232, 348, 408, 592, 736, 760, 780, 832, 952, 984, 1032, 1048, 1068, 1128, 1232, 1272, 1312, 1332, 1428, 1432, 1488, 1552, 1608, 1692, 1912, 2052, 2200, 2272, 2292, 2436, 2484, 2552, 2576, 2608, 2632, 2700, 2728, 2832, 2848, 3048, 3088

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			12 = phi(13) = phi(21) = phi(26) = phi(28) = phi(36) = phi(42).
		

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), this sequence (6), A060670 (7), A060671 (8), A060672 (9), A060673 (10), A060674 (11), A060675 (12).

Programs

Mathematica

a = Table[ 0, {4000} ]; Do[ p = EulerPhi[ n ]; If[ p < 4001, a[ [ p ] ]++ ], {n, 1, 15000} ]; Select[ Range[ 4000 ], a[ [ # ] ] == 6 & ]
Take[Select[Tally[EulerPhi[Range[50000]]],#[[2]]==6&][[All,1]]//Sort,50] (* Harvey P. Dale, Sep 15 2016 *)

PARI

is(n)=sum(i=1,n,eulerphi(i)==n)==6 \\ Charles R Greathouse IV, Mar 03 2014

PARI

is(k) = invphiNum(k) == 6 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp