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

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

1,1

Comments

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

Links

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

Example

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

Mathematica

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 *)

Prog

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

Crossrefs

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

Sequence in context: A271550 A315224 A315225 * A347047 A057885 A315226

Adjacent sequences: A068011 A068012 A068013 * A068015 A068016 A068017

Keyword

nonn

Author

Labos Elemer, Feb 08 2002

Status

approved