A060667 Numbers k such that phi(x) = k has exactly 4 solutions.

4, 6, 18, 42, 100, 162, 184, 208, 328, 424, 460, 468, 486, 492, 616, 636, 664, 688, 700, 712, 784, 820, 900, 904, 1020, 1060, 1072, 1168, 1240, 1264, 1276, 1288, 1300, 1356, 1360, 1384, 1404, 1458, 1480, 1528, 1672, 1740, 1768, 1864, 1896, 1900, 1908, 2008

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			18 = phi(19) = phi(27) = phi(38) = phi(54).
		

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), this sequence (4), A060668 (5), A060669 (6), A060670 (7), A060671 (8), A060672 (9), A060673 (10), A060674 (11), A060675 (12).

Programs

Mathematica

a = Table[ 0, {2500} ]; Do[ p = EulerPhi[ n ]; If[ p < 2501, a[ [ p ] ]++ ], {n, 1, 5000} ]; Select[ Range[ 2500 ], a[ [ # ] ] == 4 & ]

PARI

is(k) = invphiNum(k) == 4 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp