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

Cf. A030078, A251720.

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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)

Cf. A030078, A251720

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

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

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8, 12, 18, 27, 45, 75, 125, 175, 245, 343, 539, 847, 1331, 1573, 1859, 2197, 2873, 3757, 4913, 5491, 6137, 68416859, 8303, 10051, 12167, 15341, 19343, 24389, 26071, 27869, 29791, 35557, 42439, 50653, 56129, 62197, 68921, 72283, 75809, 79507, 86903, 94987, 103823

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 *)

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

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Jeff Burch (jmburch(AT)osprey.smcm.edu)

Jeff Burch

OEIS Server: https://oeis.org/edit/global/1923

nonn,new

nonn

Jeff Burch (jmburch@(AT)osprey.smcm.edu)