A055971 Numbers k such that k | (sigma(k) - d(k) - phi(k)) and k is not a prime or twice a prime.

1, 198, 294, 20280, 195320, 1782240, 3038720, 12190720

Offset: 1

Author

Robert G. Wilson v, Jul 19 2000

Keywords

• nonn
• more

Comments

a(9) > 10^10, if it exist. - Amiram Eldar, Apr 29 2024

Crossrefs

Cf. A000005 (d(n)), A000010 (phi), A000203 (sigma).

Programs

Mathematica

Do[ If[ And[ !PrimeQ[ n ], !PrimeQ[ n/2 ] ], If[ Mod[ DivisorSigma[ 1, n ]-DivisorSigma[ 0, n ]- EulerPhi[ n ], n ]==0, Print[ n ] ] ], {n, 1, 10^8} ]

PARI

is1(k) = {my(f = factor(k)); !((sigma(f) - numdiv(f) - eulerphi(f)) % k);}
is(k) = !isprime(k) && !(!(k%2) && isprime(k/2)) && is1(k); \\ Amiram Eldar, Apr 29 2024