A039789 Integers k such that phi(k) is equal to the product of (the sum of prime factors and the sum of exponents) of k+1.

7, 15, 62, 65, 76, 98, 260, 980

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• more

Comments

Next term if it exists is greater than 1500000. - Reiner Martin, May 20 2001

No further terms up to 20000000. - Harvey P. Dale, Apr 19 2013

a(9) > 10^10, if it exists. - Amiram Eldar, Jun 10 2025

Examples

			62 is a term since phi(62) = 30, 63 = 3^2*7^1, (3+7)*(2+1) = 30.
		

Crossrefs

Cf. A000010, A039697, A039774, A039788.

Programs

Mathematica

epQ[n_]:=Module[{fi=Transpose[FactorInteger[n+1]]},EulerPhi[n]== Total[ First[fi]]* Total[Last[fi]]]; Select[Range[1000],epQ] (* Harvey P. Dale, Apr 19 2013 *)

PARI

isok(k) = my(f=factor(k+1)); eulerphi(k) == vecsum(f[,1]) * vecsum(f[,2]); \\ Michel Marcus, Oct 30 2022