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

Author

Vladimir Joseph Stephan Orlovsky, Oct 26 2009

Keywords

• nonn

Comments

Intersection of A143610 and A124936.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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(nKlaus Brockhaus, Oct 29 2009

Extensions

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