A166988 Products n of a square of a prime and a cube of a prime such that n-1 and n+1 are semiprimes.

392, 14792, 19652, 48668, 55112, 197192, 291848, 783752, 908552, 963272, 1203052, 1541768, 1670792, 5081672, 5903048, 8193532, 9732872, 10089032, 10285412, 12241352, 13333448, 13960328, 14087432, 14818568, 15882248, 16290632

Offset

1,1

Comments

Intersection of A143610 and A124936.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..112

Example

392 = 7^2*2^3; 391 = 17*23 and 393 = 3*131 are semiprimes, hence 392 is in the sequence.
14792 = 2^3*43^2 is in the sequence because 14791=7*2113 and 14793=3*4931 are semiprimes.

Mathematica

f2[n_]:=Last/@FactorInteger[n]=={2, 3}||Last/@FactorInteger[n]=={3, 2}; f1[n_]:=Plus@@Last/@FactorInteger[n]==2; lst={}; Do[If[f2[n], If[f1[n-1]&&f1[n+1], AppendTo[lst, n]]], {n, 10!}]; lst
With[{prs=Prime[Range[300]]}, Union[Select[Times@@@Tuples[{prs^2, prs^3}], PrimeOmega[#-1] == PrimeOmega[#+1]==2&]]] (* Harvey P. Dale, Aug 13 2013 *)

Prog

(PARI) {m=17000000; v=[]; forprime(j=2, sqrtint(m\8), a=j^2; g=sqrtn(m\a, 3); forprime(k=2, g, n=a*k^3; if(n<m, if(bigomega(n-1)==2&&bigomega(n+1)==2, v=concat(v, n))))); Vec(listsort(List(v), 1))} \\ Klaus Brockhaus, Oct 29 2009

Crossrefs

Cf. A001248 (squares of primes), A030078 (cubes of primes), A001358 (semiprimes).

Sequence in context: A235313 A203917 A180295 * A264311 A035751 A107547

Adjacent sequences: A166985 A166986 A166987 * A166989 A166990 A166991

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Oct 26 2009

Extensions

Edited by Klaus Brockhaus and R. J. Mathar, Oct 28 2009

Status

approved