A060672 Numbers k such that phi(x) = k has exactly 9 solutions.

40, 60, 108, 128, 252, 276, 440, 612, 696, 996, 1088, 1380, 1500, 1824, 1860, 1932, 2064, 2472, 2796, 2928, 3060, 3132, 3384, 3516, 4584, 4932, 5076, 5136, 5436, 5700, 5888, 6096, 6372, 6640, 6744, 7020, 7080, 7380, 7452, 7476, 7704, 8040, 8676, 8892

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			40 = phi(41) = phi(55) = phi(75) = phi(82) = phi(88) = phi(100) = phi(110) = phi(132) = phi(150).
		

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), this sequence (9), A060673 (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[ [ # ] ] == 9 & ]

PARI

is(n)=sum(i=1,n,eulerphi(i)==n)==9 \\ Charles R Greathouse IV, Mar 03 2014

PARI

is(k) = invphiNum(k) == 9 \\ Amiram Eldar, Nov 17 2024, using Max Alekseyev's invphi.gp