A350284 Numbers k which are the product of a cube greater than 1 and a prime, and where k-1 and k-2 are semiprimes.

16, 40, 88, 135, 328, 448, 1048, 1384, 1715, 1984, 2104, 2560, 2943, 3064, 3904, 4288, 5184, 5319, 6507, 6939, 7000, 7263, 7864, 8728, 9099, 9288, 9664, 11043, 11367, 12288, 15579, 17496, 17944, 18808, 22599, 23488, 24875, 25083, 25407, 26008, 26584, 30184, 30904, 31288, 31944

Offset

1,1

Comments

Since there are an infinite number of semiprimes, there may be an infinite number of such numbers k. k=16 appears to be the only solution where the prime is 2.

Links

Table of n, a(n) for n=1..45.

Example

k=16 is a term: 16 = 2^3 * 2, 15 = 3*5, and 14 = 2*7.

Mathematica

q[n_] := ! PrimeQ[n] && Plus @@ Mod[FactorInteger[n][[;; , 2]], 3] == 1 && PrimeOmega[{n - 2, n - 1}] == {2, 2}; Select[Range[32000], q] (* Amiram Eldar, Dec 28 2021 *)

Prog

(PARI) isok(n)=my(s=factor(n)[, 2]~); select(e->e<>0, s%3)==[1] && s<>[1] && bigomega(n-1)==2 && bigomega(n-2)==2 \\ Andrew Howroyd, Dec 24 2021

Crossrefs

Cf. A000578 (cubes), A001358 (semiprimes).

Sequence in context: A258258 A086046 A184030 * A182461 A205065 A368078

Adjacent sequences: A350281 A350282 A350283 * A350285 A350286 A350287

Keyword

nonn

Author

Sheldon Collier, Dec 23 2021

Status

approved