A033477 Products p^3 or p^2*q, where {p,q} are consecutive primes.

8, 12, 18, 27, 45, 75, 125, 175, 245, 343, 539, 847, 1331, 1573, 1859, 2197, 2873, 3757, 4913, 5491, 6137, 6859, 8303, 10051, 12167, 15341, 19343, 24389, 26071, 27869, 29791, 35557, 42439, 50653, 56129, 62197, 68921, 72283, 75809, 79507, 86903, 94987, 103823

Offset: 0

Author

Jeff Burch

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A030078, A251720.

Programs

Maple

R:= NULL: p:= 2:
for n from 1 to 30 do
  q:= nextprime(p);
  R:= R, p^3, p^2*q, p*q^2;
  p:= q;
od:
R; # Robert Israel, Jun 26 2020

Mathematica

nn=50;With[{prs=Prime[Range[nn]]},Take[Union[Flatten[{prs^3,{#[[1]]^2 #[[2]],#[[2]]^2 #[[1]]}&/@Partition[prs,2,1]}]],nn]] (* Harvey P. Dale, Dec 28 2013 *)

Formula

From Robert Israel, Jun 26 2020: (Start)

a(3k) = A030078(k+1).

a(3k+1) = A251720(k+1).

a(3k+2) = a(3k+1)^2/a(3k). (End)

Extensions

Corrected and extended by Harvey P. Dale, Dec 28 2013