A378506 The number of solutions to the equation phi(phi(x)) = n, where phi is the Euler totient function.

5, 8, 0, 13, 0, 4, 0, 23, 0, 2, 0, 14, 0, 0, 0, 36, 0, 2, 0, 5, 0, 2, 0, 32, 0, 0, 0, 2, 0, 0, 0, 54, 0, 0, 0, 11, 0, 0, 0, 23, 0, 0, 0, 5, 0, 0, 0, 66, 0, 0, 0, 2, 0, 4, 0, 3, 0, 0, 0, 2, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 41, 0, 2, 0, 6

Offset

1,1

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.

Formula

a(n) > 0 if and only if n is in A378508.

Mathematica

a[n_] := Sum[PhiMultiplicity[i], {i, PhiInverse[n]}]; Array[a, 100] (* using David M. Bressoud's CNT.m *)

Prog

(PARI) a(n) = vecsum(apply(x -> invphiNum(x), invphi(n))); \\ using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000010, A010554, A014197, A378507, A378508.

Sequence in context: A140249 A335928 A081564 * A199073 A199069 A020797

Adjacent sequences: A378503 A378504 A378505 * A378507 A378508 A378509

Keyword

nonn,easy

Author

Amiram Eldar, Nov 29 2024

Status

approved