A067351 Numbers k such that sigma(k) + phi(k) has exactly 2 distinct prime divisors.

3, 5, 6, 7, 10, 11, 13, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 37, 39, 40, 41, 42, 43, 44, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 64, 66, 67, 68, 71, 72, 73, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 87, 89, 91, 92, 93, 95, 96, 97

Offset: 1

Author

Labos Elemer, Jan 17 2002

Keywords

• nonn

Examples

			Includes all odd primes and some composites; e.g., 21 and 25, since sigma(21) + phi(21) = 32 + 12 = 44 = 2*2*11; sigma(25) + phi(25) = 31 + 20 = 51 = 3*17.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A000010, A000203, A001221, A065387, A067349, A067350.

Programs

Mathematica

Select[ Range[ 1, 100 ], Length[ FactorInteger[ DivisorSigma[ 1, # ]+EulerPhi[ # ] ] ]==2& ]
Select[Range[500], PrimeNu[EulerPhi[#] + DivisorSigma[1, #]] == 2 &] (* G. C. Greubel, May 08 2017 *)

Formula

a(n) = A001221(A000010(n) + A000203(n)) = A001221(A065387(n)) = 2.

Extensions

Edited by Dean Hickerson, Jan 20 2002