A033855 Numbers k such that j(k)*phi(k) = s(phi(k)), where j(k) = A033831(k), s(k) = sigma(k) - k.

1, 2, 7, 9, 29, 143, 155, 183, 731, 791, 1011, 1346, 35659, 60484, 65524, 525227, 525557, 525617, 526697, 529817, 531779, 567437, 1047554, 2541679, 33550337, 214486281, 1476844097, 1478227937, 1543409687, 14200144243, 14200244477, 14200257551, 14200349281, 14200779611, 14201040053, 14201501401

Offset: 1

Author

Naohiro Nomoto

Keywords

• nonn

Comments

phi(a(n)) is a multiperfect number (A007691). - Max Alekseyev, Oct 09 2023

Links

• Max Alekseyev, Table of n, a(n) for n = 1..50000

Crossrefs

Cf. A000010, A000203, A001065, A007691, A033831, A033856.

Programs

Mathematica

j[n_] := DivisorSum[n, 1&, # > 2 && n/# < #-1 &]; aQ[n_] := j[n] * (p = EulerPhi[ n]) == DivisorSigma[1, p] - p; Select[Range[10^4], aQ] (* Amiram Eldar, Jul 01 2019 *)

Extensions

More terms from Amiram Eldar, Jul 01 2019

Terms a(27) onward from Max Alekseyev, Oct 09 2023