A378509 Totient numbers k for which there is no solution to the equation phi(phi(x)) = k.

30, 42, 46, 58, 66, 70, 78, 102, 106, 110, 116, 126, 136, 138, 140, 148, 150, 166, 196, 198, 210, 222, 226, 228, 262, 268, 270, 282, 294, 296, 306, 310, 316, 330, 332, 342, 346, 366, 372, 378, 382, 388, 392, 438, 444, 452, 456, 460, 462, 466, 478, 498, 502, 506

Offset: 1

Author

Amiram Eldar, Nov 29 2024

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
• David M. Bressoud, A Course in Computational Number Theory (web page), CNT.m, Computational Number Theory Mathematica package.

Crossrefs

Intersection of A002202 (totient numbers) and the complement of A378508.

Cf. A000010, A010554, A378510.

Programs

Mathematica

q[k_] := Module[{v = PhiInverse[k]}, Length[v] > 0 && AllTrue[v, PhiMultiplicity[#] == 0 &]]; Select[Range[1000], q] (* using David M. Bressoud's CNT.m *)

PARI

is(k) = {my(v = invphi(k)); if(#v == 0, return(0)); for(i = 1, #v, if(istotient(v[i]), return(0))); 1;} \\ using Max Alekseyev's invphi.gp