A296214 Numbers k for which there is at least one x < k such that phi(x) = phi(k).

2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115

Offset: 1

Author

Antti Karttunen, Dec 08 2017

Keywords

• nonn

Comments

Numbers k for which A081373(k) > 1.

Apart from the initial term 2, this is the complement of union of A000040 (primes) and A069823.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12973
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000010, A069822, A069823, A081373.

Cf. A296087 (a subsequence).

Programs

PARI

for(n=1,200,y=0;s=eulerphi(n);for(k=1,(n-1),if(eulerphi(k)==s,y=1;break)); if(y,print1(n,",")));

PARI

is(k) = invphiMin(eulerphi(k)) < k; \\ Amiram Eldar, Nov 15 2024, using Max Alekseyev's invphi.gp