A061367 Composite n such that sigma(n)-phi(n) divides sigma(n)+phi(n).

15, 35, 95, 119, 143, 209, 287, 319, 323, 357, 377, 527, 559, 779, 899, 923, 989, 1007, 1045, 1189, 1199, 1343, 1349, 1763, 1919, 2159, 2261, 2507, 2639, 2759, 2911, 3239, 3339, 3553, 3599, 3827, 4031, 4147, 4607, 5049, 5183, 5207, 5249, 5459, 5543, 6439

Offset: 1

Author

Joseph L. Pe, Feb 13 2002

Keywords

• nonn

Comments

Primes trivially satisfy the defining condition.

Examples

			sigma(15)-phi(15) = 24-8 = 16 divides sigma(15)-phi(15)=24+8 = 32, so 15 is a term of the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051612, A065387.

Programs

Mathematica

f[n_] := Module[{a = DivisorSigma[1, n], b = EulerPhi[n]}, Mod[(a + b), (a - b)] == 0]; Select[Range[2, 10^4], (f[ # ] && ! PrimeQ[ # ]) &]
cnQ[n_]:=With[{s=DivisorSigma[1,n],p=EulerPhi[n]},Mod[s+p,s-p]==0]; Select[Range[6500],CompositeQ[#]&&cnQ[#]&] (* Harvey P. Dale, Jun 14 2025 *)

Formula

It seems that a(n) is asymptotic to c*n^2, 22*n^2. - Benoit Cloitre, Sep 17 2002