A121307 Products of three terms from A003627.

8, 20, 44, 50, 68, 92, 110, 116, 125, 164, 170, 188, 212, 230, 236, 242, 275, 284, 290, 332, 356, 374, 404, 410, 425, 428, 452, 470, 506, 524, 530, 548, 575, 578, 590, 596, 605, 638, 668, 692, 710, 716, 725, 764, 782, 788, 830, 890, 902, 908, 932, 935, 956

Offset

1,1

Comments

It would be incorrect to call these Eisenstein 3-almost primes. For the Eisenstein primes see A055664. - N. J. A. Sloane, Feb 06 2008.

References

J. H. Conway and R. K. Guy, The Book of Numbers. New York: Springer-Verlag, pp. 220-223, 1996.

Stan Wagon, "Eisenstein Primes," Section 9.8 in Mathematica in Action. New York: W. H. Freeman, pp. 319-323, 1991.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Mathematica

ok[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f == 3 && Max@ Mod[1 + First /@ f, 3] == 0]; Select[Range@ 1000, ok] (* Giovanni Resta, Jun 12 2016 *)

Prog

(PARI) list(lim)=my(v=List(), u=v, t); forprime(p=2, lim\4, if(p%3==2, listput(u, p))); for(i=1, #u, for(j=i, #u, if(u[i]*u[j]^2>lim, break); for(k=j, #u, t=u[i]*u[j]*u[k]; if(t>lim, break); listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017
(Python)
from sympy import primerange
from itertools import combinations_with_replacement as mc
def aupto(limit):
    terms = [p for p in primerange(2, limit//4+1) if p%3 == 2]
    return sorted(set(a*b*c for a, b, c in mc(terms, 3) if a*b*c <= limit))
print(aupto(957)) # Michael S. Branicky, Aug 20 2021

Crossrefs

Cf. A003627, A014612, A112770.

Sequence in context: A318071 A308904 A192753 * A338471 A086169 A273241

Adjacent sequences: A121304 A121305 A121306 * A121308 A121309 A121310

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 05 2006

Extensions

Definition corrected by N. J. A. Sloane, Feb 06 2008

a(37)-a(53) from Giovanni Resta, Jun 12 2016

Status

approved