A390049 Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k).

40, 208, 928, 3904, 260608, 1045504, 16764928, 268386304

Offset

1,1

Comments

Includes 2^k * (2^k - 3) for k in A050414. Are there any other terms? - Robert Israel, Nov 11 2025

Links

Table of n, a(n) for n=1..8.

Example

40 is in the sequence since sigma(40) = 90 = 72 + 16 + 2 = psi(40) + phi(40) + omega(40).

Maple

filter:= proc(n) local F, sigma, psi, tau, t;
 F:= ifactors(n)[2];
 sigma:= mul((t[1]^(1+t[2])-1)/(t[1]-1), t=F);
 psi:= n * mul(1+1/t[1], t=F);
 phi:= n * mul(1-1/t[1], t=F);
 omega:= nops(F);
 sigma = psi + phi + omega
end proc:
select(filter, [$1..10^8]); # Robert Israel, Nov 11 2025

Mathematica

psi[n_] := n*Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Select[Range[1.1*10^6], DivisorSigma[1, #] == psi[#] + EulerPhi[#] + PrimeNu[#] &] (* Amiram Eldar, Oct 23 2025 *)

Crossrefs

Cf. A000203 (sigma), A001615 (psi), A000010 (phi), A001221 (omega), A050414.

Cf. A386637, A388001, A389855, A389856.

Sequence in context: A387645 A247405 A235270 * A181637 A111176 A072108

Adjacent sequences: A390046 A390047 A390048 * A390050 A390051 A390052

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Oct 22 2025

Extensions

a(7)-a(8) from Amiram Eldar, Oct 23 2025

Status

approved