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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000203, A072282.

Sequence in context: A015783 A356055 A300020 * A270544 A181995 A169810

Adjacent sequences: A068014 A068015 A068016 * A068018 A068019 A068020

Keyword

nonn

Author

Labos Elemer, Feb 08 2002

Status

approved