A068017 Composite n such that sigma(n) - 1 and sigma(n) + 1 are twin primes.

6, 10, 20, 24, 26, 30, 38, 46, 51, 55, 85, 88, 105, 114, 118, 126, 135, 136, 141, 145, 147, 155, 158, 161, 177, 178, 185, 203, 206, 207, 209, 216, 230, 236, 238, 255, 278, 296, 321, 344, 346, 355, 371, 377, 384, 391, 396, 398, 416, 424, 447, 462, 486, 500

Offset: 1

Author

Labos Elemer, Feb 08 2002

Keywords

• nonn

Examples

			For n=46, sigma(46)=1+2+23+46=72, for n=51, sigma(51)=1+3+17+51=72 and also for n=55, sigma(55)=1+5+11+55=72 is the middle term of {71,73} twins.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A072282.

Programs

Mathematica

Do[s=-1+DivisorSigma[1, n]; s1=1+DivisorSigma[1, n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[n]], {n, 1, 2000}]
cntpQ[n_]:=Module[{ds=DivisorSigma[1,n]},CompositeQ[n]&&AllTrue[ds+{1,-1}, PrimeQ]]; Select[Range[500],cntpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 05 2015 *)

PARI

isok(n) = my(s=sigma(n)); !isprime(n) && isprime(s-1) && isprime(s+1); \\ Michel Marcus, Apr 24 2019