A066071 -id:A066071 - cp's OEIS frontend

A078893 Composite numbers k such that phi(k) - 1 is prime, where phi is Euler's totient function (A000010).

8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 26, 27, 28, 30, 33, 35, 36, 38, 39, 42, 44, 45, 49, 50, 51, 52, 54, 56, 62, 64, 65, 66, 68, 69, 70, 72, 77, 78, 80, 81, 84, 86, 90, 91, 92, 93, 95, 96, 98, 99, 102, 104, 105, 111, 112, 117, 120, 121, 122, 123, 124, 129, 130, 133

Offset: 1

Reinhard Zumkeller, Dec 12 2002

nonn

A078892 with the primes removed. - Ray Chandler, May 26 2008

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

Cf. A000010, A000040, A008864, A109606, A078892, A066071, A068019.

Select[Range[150],CompositeQ[#]&&PrimeQ[EulerPhi[#]-1]&] (* Harvey P. Dale, Dec 28 2021 *)

is(n)=!isprime(n) && isprime(eulerphi(n)-1) \\ Charles R Greathouse IV, Feb 21 2013

A068014 Nonprimes n such that 1+phi(n) and -1 + sigma(n) are prime numbers.

Original entry on oeis.org

6, 10, 14, 21, 26, 34, 38, 40, 46, 55, 57, 58, 60, 63, 74, 76, 86, 88, 93, 111, 114, 117, 118, 124, 126, 135, 145, 153, 158, 166, 178, 184, 186, 190, 194, 198, 206, 208, 209, 216, 221, 224, 230, 232, 238, 250, 252, 254, 260, 266, 270, 278, 280, 295, 297, 298

Offset: 1

Labos Elemer, Feb 08 2002

nonn

1+A000010(n) and -1+A000203(n) are primes but n is nonprime.

			For n = 38, phi(38) + 1 = 19 and sigma(38) - 1 = 1 + 2 + 19 + 38 - 1 = 59. [corrected by _Peter Munn_, Dec 30 2017]

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000010, A000203, A058339, A058340, A066071, A066072, A066073, A066074, A066075, A066076, A066077, A066080.

Do[s=-1+DivisorSigma[1, n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[{n, s1, s}]], {n, 1, 1000}] (* generates sequence and related primes too *)
Select[Range@ 300, And[CompositeQ@ #, AllTrue[{1 + EulerPhi@ #, -1 + DivisorSigma[1, #]}, PrimeQ]] &] (* Michael De Vlieger, Dec 29 2017 *)

isok(n) = !isprime(n) && isprime(1+eulerphi(n)) && isprime(sigma(n)-1); \\ Michel Marcus, Dec 29 2017

cp's OEIS Frontend

A078893 Composite numbers k such that phi(k) - 1 is prime, where phi is Euler's totient function (A000010).

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