A068414 Numbers k such that sigma(k) = 3k - 2*phi(k).

1, 12, 56, 260, 992, 1976, 2156, 2754, 16256, 25232, 41072, 133984, 145888, 1100864, 1270208, 1439552, 2237888, 4729664, 67100672, 75398912, 171627376, 277060144, 473089984, 538178048, 558585344, 629225984, 1192258048, 1863840112, 2181070592, 4534854656

Offset: 1

Author

Benoit Cloitre, Mar 03 2002

Keywords

• nonn

Comments

If 2^p-1 is prime (a Mersenne prime) and n = 2^p*(2^p-1) then n is in the sequence because 3*n-2*phi(n) = 3*2^p*(2^p-1)-2^p*(2^p-2) = 2^p*(2^(p+1)-1) = sigma(2^p-1)*sigma(2^p) = sigma(2^p*(2^p-1)) = sigma(n). - Farideh Firoozbakht, Dec 31 2005

Crossrefs

Cf. A000010, A000203, A068418, A069719, A069737.

Programs

Mathematica

Select[Range[10^6], DivisorSigma[1, #] == 3*# - 2*EulerPhi[#] &] (* Amiram Eldar, May 14 2022 *)

PARI

for(n=1,500000, if(sigma(n)==3*n-2*eulerphi(n),print1(n,",")))

Extensions

More terms (complete up to 50000000). - Rick L. Shepherd, Mar 28 2002

More terms from Labos Elemer, Apr 03 2002

a(24)-a(30) from Donovan Johnson, Feb 08 2012