A067260 Numbers k such that sigma(k+1) = 2*phi(k).

13, 43, 109, 151, 589, 883, 2143, 2725, 4825, 4921, 9541, 13189, 21637, 22249, 22489, 29971, 30229, 33787, 36247, 72541, 73513, 83287, 94489, 109213, 113269, 117367, 189103, 190489, 198457, 216529, 247597, 277447, 297307, 320137, 353821, 357751, 376753, 391543

Offset: 1

Author

Benoit Cloitre, Feb 21 2002

Keywords

• nonn

Comments

If p=2^n+3 and both numbers p & q=(1/2)*(p^2-3p-2) are primes then q is in the sequence, because sigma(q+1)=sigma((1/2)*(p-3)*p)= sigma(2^(n-1)*p)=(2^n-1)*(p+1)=(p-4)*(p+1)=p^2-3p-4=2q-2=2*phi(q). 13, 43, 151, 2143 & 34360131583 are such terms corresponding to n = 2, 3, 4, 6 & 18. - Farideh Firoozbakht, Feb 16 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A000203, A067261, A067262, A067263, A135241.

Programs

Mathematica

Do[If[DivisorSigma[1,n+1]==2*EulerPhi@n,Print[n]],{n,200000}] (* Farideh Firoozbakht, Feb 16 2008 *)

Extensions

More terms from Amiram Eldar, Apr 24 2022