A060672 - OEIS

%I #14 Nov 17 2024 07:20:01

%S 40,60,108,128,252,276,440,612,696,996,1088,1380,1500,1824,1860,1932,

%T 2064,2472,2796,2928,3060,3132,3384,3516,4584,4932,5076,5136,5436,

%U 5700,5888,6096,6372,6640,6744,7020,7080,7380,7452,7476,7704,8040,8676,8892

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

%H Amiram Eldar, <a href="/A060672/b060672.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

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

%t a = Table[ 0, {10000} ]; Do[ p = EulerPhi[ n ]; If[ p < 10001, a[ [ p ] ]++ ], {n, 1, 35000} ]; Select[ Range[ 10000 ], a[ [ # ] ] == 9 & ]

%o (PARI) is(n)=sum(i=1,n,eulerphi(i)==n)==9 \\ _Charles R Greathouse IV_, Mar 03 2014

%o (PARI) is(k) = invphiNum(k) == 9 \\ _Amiram Eldar_, Nov 17 2024, using _Max Alekseyev_'s invphi.gp

%Y Cf. A000010.

%Y 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).

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Apr 18 2001