A067349 -id:A067349 - cp's OEIS frontend

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

Labos Elemer, Jan 17 2002

nonn

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.

			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.

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

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

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

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

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

Edited by Dean Hickerson, Jan 20 2002

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

Original entry on oeis.org

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

Labos Elemer, Jan 17 2002

nonn

			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.

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

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

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

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

Edited by Dean Hickerson, Jan 20 2002

cp's OEIS Frontend

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

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