A060671 Numbers k such that phi(x) = k has exactly 8 solutions.

36, 64, 176, 200, 224, 280, 324, 464, 520, 888, 920, 1184, 1368, 1400, 1520, 1696, 1720, 1904, 1960, 2040, 2096, 2120, 2256, 2392, 2600, 2656, 2712, 2752, 2864, 2944, 2960, 2968, 2976, 2988, 3104, 3276, 3300, 3408, 3616, 3640, 3792, 3800, 3816, 3824, 3880

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			36 = phi(37) = phi(57) = phi(63) = phi(74) = phi(76) = phi(108) = phi(114) = phi(126).
		

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), this sequence (8), A060672 (9), A060673 (10), A060674 (11), A060675 (12).

Programs

Mathematica

a = Table[ 0, {5000} ]; Do[ p = EulerPhi[ n ]; If[ p < 5001, a[ [ p ] ]++ ], {n, 1, 25000} ]; Select[ Range[ 5000 ], a[ [ # ] ] == 8 & ]

PARI

is(n)=sum(i=1,n,eulerphi(i)==n)==8 \\ Charles R Greathouse IV, Mar 03 2014

PARI

is(k) = invphiNum(k) == 8 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp