A067532 -id:A067532 - cp's OEIS frontend

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

Amarnath Murthy, Feb 17 2002

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

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

Intersection of A067531 and A067532.

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

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

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

A158458 Numbers k such that k + bigomega(k) is prime.

Original entry on oeis.org

2, 8, 9, 15, 20, 21, 28, 32, 35, 39, 44, 48, 50, 51, 57, 65, 68, 69, 70, 76, 77, 87, 95, 98, 108, 110, 111, 124, 129, 135, 148, 154, 155, 161, 162, 164, 168, 170, 176, 177, 188, 189, 190, 192, 209, 221, 225, 230, 236, 237, 238, 249, 252, 264, 266, 267, 268, 272, 290

Offset: 1

Juri-Stepan Gerasimov, Mar 19 2009

nonn

2 is the only prime number in the sequence. - Michel Lagneau, May 17 2010

			a(2) = 8 = 2*2*2; 8+3 = 11 is prime.
a(3) = 9 = 3*3; 9+2 = 11 is prime.
a(4) = 15 = 3*5; 15+2 = 17 is prime.

Eric Chen, Table of n, a(n) for n = 1..10000

Cf. A000040, A001222.

Cf. A067532, A078762, A068080. - Michel Lagneau, May 17 2010

for k from 2 to 400 do if isprime(k+numtheory[bigomega](k)) then printf("%d,",k) ; fi; od: # R. J. Mathar, May 19 2009, May 23 2010

Select[Range[10^3], PrimeQ[ # + Plus @@ Last /@ FactorInteger[ # ]] &] (* Michel Lagneau, May 17 2010 *)
Select[Range[300],PrimeQ[#+PrimeOmega[#]]&] (* Harvey P. Dale, Dec 20 2021 *)

is(n)=isprime(n+bigomega(n)) \\ Eric Chen, Jun 13 2018

{k: k+A001222(k) in A000040}.

191 replaced with 192 and extended by R. J. Mathar, May 19 2009

Generalized (by inserting a(1)=2) by Michel Lagneau, May 17 2010

cp's OEIS Frontend

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

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