A068484 Numbers k that divide phi(k)^2 + sigma(k)^2.

1, 2, 10, 45, 65, 180, 212, 222, 369, 588, 810, 864, 1274, 1521, 1836, 2548, 2940, 3114, 3552, 4770, 5496, 5684, 6027, 6642, 8820, 9140, 10464, 10614, 13311, 14688, 15210, 20737, 21600, 22776, 26900, 27000, 27270, 28476, 28518, 42212, 42336

Offset: 1

Author

Benoit Cloitre, Mar 10 2002

Keywords

• easy
• nonn

Comments

a(275) > 7*10^7. - G. C. Greubel, Oct 15 2018

Links

• G. C. Greubel, Table of n, a(n) for n = 1..274

Crossrefs

Cf. A072861 (sigma(n)^2), A127473 (phi(n)^2).

Programs

GAP

Filtered([1..42500],n->(Phi(n)^2+Sigma(n)^2) mod n=0); # Muniru A Asiru, Oct 16 2018

Maple

with(numtheory): select(n->modp(phi(n)^2+sigma(n)^2,n)=0,[$1..42500]); # Muniru A Asiru, Oct 16 2018

Mathematica

Select[Range[7000], IntegerQ[(EulerPhi[#]^2 + DivisorSigma[1, #]^2)/#] &] (* G. C. Greubel, Oct 15 2018 *)