A072282 Numbers n such that sigma(n) + 1 and sigma(n) - 1 are twin primes.

3, 5, 6, 10, 11, 17, 20, 24, 26, 29, 30, 38, 41, 46, 51, 55, 59, 71, 85, 88, 101, 105, 107, 114, 118, 126, 135, 136, 137, 141, 145, 147, 149, 155, 158, 161, 177, 178, 179, 185, 191, 197, 203, 206, 207, 209, 216, 227, 230, 236, 238, 239, 255, 269, 278, 281, 296

Offset: 1

Author

Joseph L. Pe, Jul 10 2002

Keywords

• easy
• nonn

Examples

			sigma(20) + 1 = 43 and sigma(20) - 1 = 41, so 20 is a term of the sequence.
		

Links

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

Crossrefs

Cf. A000203, A068017.

Programs

Mathematica

Select[Range[10^3], PrimeQ[DivisorSigma[1, # ] + 1] && PrimeQ[DivisorSigma[1, # ] - 1] &]
Select[Range[300],AllTrue[DivisorSigma[1,#]+{1,-1},PrimeQ]&] (* Harvey P. Dale, Apr 06 2023 *)

PARI

isok(n) = my(p=sigma(n)-1); isprime(p) && isprime(p+2); \\ Michel Marcus, Sep 30 2019

Extensions

More terms from Amiram Eldar, Sep 30 2019