A067533 Numbers k such that both k - tau(k) and k + tau(k) are prime where tau(k) = A000005(k).

5, 15, 27, 33, 57, 93, 105, 165, 177, 189, 231, 237, 245, 267, 275, 285, 345, 375, 393, 425, 453, 555, 567, 573, 597, 609, 637, 651, 687, 723, 833, 933, 1005, 1025, 1095, 1167, 1209, 1221, 1227, 1293, 1311, 1431, 1445, 1479, 1491, 1527, 1551, 1563, 1573

Offset: 1

Author

Amarnath Murthy, Feb 17 2002

Keywords

• easy
• nonn

Examples

			57 is a term as tau(57) = 4 and 57-4 = 53 and 57+4 = 61 are both primes.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 1..1128

Crossrefs

Intersection of A067531 and A067532.

Programs

Mathematica

Select[Range[2000],With[{t=DivisorSigma[0,#]},AllTrue[#+{t,-t},PrimeQ]&]]  (* Harvey P. Dale, Mar 16 2025 *)

PARI

isok(n) = my(nd = numdiv(n)); isprime(n-nd) && isprime(n+nd); \\ Michel Marcus, Oct 12 2018

Extensions

More terms from Sascha Kurz, Mar 19 2002

Offset corrected by Alois P. Heinz, Oct 10 2018

Name changed by David A. Corneth, Oct 12 2018