A306298 Numbers k such that k^2-1 is divisible by exactly two distinct primes.

4, 5, 6, 7, 8, 9, 10, 12, 15, 17, 18, 24, 26, 28, 30, 33, 42, 48, 60, 63, 72, 80, 82, 102, 108, 126, 138, 150, 168, 180, 192, 198, 228, 240, 242, 255, 270, 282, 312, 348, 360, 420, 432, 462, 513, 522, 570, 600, 618, 642, 660, 728, 810, 822, 828, 840, 858, 882

Offset

1,1

Comments

k^2 - 1 = (k-1)*(k+1) so for most terms, k-1 and k+1 are in A000961. - David A. Corneth, Mar 31 2019

Odd terms are either 2*p-1 where p is a Fermat prime (A019434) or 2*p+1 where p is a Mersenne prime (A000668). - Robert Israel, Mar 31 2019

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

L. J. Gerstein, A reformulation of the Goldbach conjecture, Math. Mag., 66 (1993), 44-45.

Maple

select(t -> nops(numtheory:-factorset(t+1) union numtheory:-factorset(t-1)) = 2, [$2..1000]); # Robert Israel, Mar 31 2019

Mathematica

Select[Range@ 900, PrimeNu[#^2 - 1] == 2 &] (* Michael De Vlieger, Apr 01 2019 *)

Prog

(PARI) is(n) = {omega(n^2 - 1) == 2} \\ David A. Corneth, Mar 31 2019

Crossrefs

Cf. A000961, A001221, A014574 (the "big omega" analog).

Cf. A000668, A019434.

Sequence in context: A308040 A287961 A030791 * A227763 A039091 A189817

Adjacent sequences: A306295 A306296 A306297 * A306299 A306300 A306301

Keyword

nonn

Author

N. J. A. Sloane, Mar 31 2019

Status

approved