A067781 Numbers k such that phi(k) and sigma(k) are both perfect squares.

1, 170, 364, 679, 5044, 5130, 5670, 5770, 8721, 8736, 9154, 9639, 9809, 14322, 16376, 22413, 27783, 30256, 32025, 37114, 38760, 51455, 71604, 78570, 82615, 88392, 92004, 100821, 101153, 104168, 115430, 121056, 133569, 139954, 148568, 171069, 177940, 198462, 217868

Offset: 1

Author

Benoit Cloitre, Feb 07 2002

Keywords

• nonn

Comments

A subsequence of A011257. - M. F. Hasler, Sep 22 2009

Links

• Donovan Johnson, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010 (phi), A000203 (sigma), A006532, A011257, A039770.

Programs

Mathematica

Select[Range[250000], And @@ (IntegerQ[Sqrt[#1]] & /@ {EulerPhi[#], DivisorSigma[1, #]} ) &] (* Amiram Eldar, May 08 2025 *)

PARI

isok(k) = {my(f = factor(k)); issquare(eulerphi(f)) && issquare(sigma(f));} \\ Amiram Eldar, May 08 2025

Formula

Equals A006532 intersect A039770. - M. F. Hasler, Sep 22 2009