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Products p^3 or p^2*q, where {p,q} are consecutive primes.
1

%I #11 Jun 26 2020 23:45:02

%S 8,12,18,27,45,75,125,175,245,343,539,847,1331,1573,1859,2197,2873,

%T 3757,4913,5491,6137,6859,8303,10051,12167,15341,19343,24389,26071,

%U 27869,29791,35557,42439,50653,56129,62197,68921,72283,75809,79507,86903,94987,103823

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

%H Robert Israel, <a href="/A033477/b033477.txt">Table of n, a(n) for n = 0..10000</a>

%F From _Robert Israel_, Jun 26 2020: (Start)

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

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

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

%p R:= NULL: p:= 2:

%p for n from 1 to 30 do

%p q:= nextprime(p);

%p R:= R, p^3, p^2*q, p*q^2;

%p p:= q;

%p od:

%p R; # _Robert Israel_, Jun 26 2020

%t 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 *)

%Y Cf. A030078, A251720.

%K nonn

%O 0,1

%A _Jeff Burch_

%E Corrected and extended by _Harvey P. Dale_, Dec 28 2013