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A068014 Nonprimes n such that 1+phi(n) and -1 + sigma(n) are prime numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A057885 A315226 A315227

Adjacent sequences:  A068011 A068012 A068013 * A068015 A068016 A068017

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 08 2002

STATUS

approved

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Last modified June 13 22:55 EDT 2021. Contains 345016 sequences. (Running on oeis4.)