A388650 Numbers k such that psi(k) = phi(k) + pi(k).

1, 3, 437, 11509, 3029573, 15714799, 15715171, 312616663, 45764089927, 2002330897321

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Example

437 is in the sequence since psi(437) = 480 = 396 + 84 = phi(437) + pi(437).

Mathematica

psi[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors[n]}]; OK[k_]:=psi[k]==EulerPhi[k]+PrimePi[k]; Select[Range[10^6], OK] (* James C. McMahon, Oct 20 2025 *)

Prog

(PARI) dedpsi(f) = prod(k = 1, #f~, (f[k, 1]+1) * f[k, 1]^(f[k, 2]-1));
list(lim) = {my(q = 2, m = 0, f); print1(1, ", "); forprime(p = 3, lim, m++; for(k = q, p-1, f = factor(k); if(dedpsi(f) == eulerphi(f) + m, print1(k, ", "))); q = p); } \\ Amiram Eldar, Oct 17 2025

Crossrefs

Cf. A000010, A000720, A001615, A067788, A387999, A388000.

Sequence in context: A086207 A326373 A092052 * A382226 A139999 A140870

Adjacent sequences: A388647 A388648 A388649 * A388651 A388652 A388653

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Oct 17 2025

Status

approved