A067350 Numbers n such that sigma(n)+phi(n) has exactly 4 divisors.

3, 5, 6, 7, 10, 11, 13, 16, 17, 19, 22, 23, 25, 27, 29, 31, 37, 40, 41, 43, 46, 47, 52, 53, 58, 59, 61, 64, 67, 68, 71, 72, 73, 79, 80, 82, 83, 89, 97, 98, 101, 103, 106, 107, 109, 113, 117, 127, 128, 131, 136, 137, 139, 144, 149, 151, 157, 162, 163, 166, 167, 169

Offset: 1

Author

Labos Elemer, Jan 17 2002

Keywords

• nonn

Comments

For all terms up to 10^12, sigma(n)+phi(n) is a product of 2 distinct primes. The only other possibility is that sigma(n)+phi(n) is a cube of a prime, for some n which is either a square or twice a square; does this occur? If not, then this sequence is contained in A067351.

Examples

			Includes all odd primes and some composites; e.g. 22 and 25, since sigma(22)+phi(22)=36+10=46=2*23 and sigma(25)+phi(25)=31+20=51=3*17.
		

Links

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

Crossrefs

Cf. A000005, A000010, A000203, A067349, A067351.

Programs

Mathematica

Select[ Range[ 1, 200 ], DivisorSigma[ 0, DivisorSigma[ 1, # ]+EulerPhi[ # ] ]==4& ]

PARI

isok(n) = numdiv(sigma(n)+eulerphi(n)) == 4; \\ Michel Marcus, Aug 13 2019

Formula

A000005(A000010(n) + A000203(n)) = A067349(n) = 4.

Extensions

Edited by Dean Hickerson, Jan 20 2002