A350375 Numbers with exactly 8 semiprime divisors.

1260, 1980, 2100, 2340, 2520, 2772, 2940, 3060, 3150, 3276, 3300, 3420, 3780, 3900, 3960, 4140, 4200, 4284, 4410, 4680, 4788, 4950, 5040, 5100, 5148, 5220, 5544, 5580, 5700, 5796, 5850, 5880, 5940, 6120, 6468, 6552, 6600, 6660, 6732, 6840, 6900, 7020, 7260, 7308

Offset

1,1

Comments

Numbers with prime signature {1,1,j,k} where j >= 2 and k >= 2. - Robert Israel, Nov 09 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 10^4: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N/(2^2*3^2*5), 2)]):
nP:= nops(P):
Res:= NULL:
for i1 from 1 to nP do
  p1:= P[i1];
  for i2 from i1+1 to nP do
    p2:= P[i2];
    if p1 * p2 * 6^2 > N then break fi;
    for i3 from 1 to nP do
      p3:= P[i3];
      if i3 = i1 or i3 = i2 then next fi;
      for n3 from 2 while p1 * p2 * p3^(n3+2) <= N do
        for i4 from i3 + 1 to nP do
          if i4 = i1 or i4 = i2 then next fi;
          p4:= P[i4];
          if p1 * p2 * p3^n3 * p4^2 > N then break fi;
          for n4 from 2 do
            x:= p1 * p2  * p3^n3 * p4^n4;
            if x > N then break fi;
            Res:= Res, x
od od od od od od:
Res:= sort([Res]); # Robert Israel, Nov 09 2025

Mathematica

q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 8; Select[Range[7500], q] (* Amiram Eldar, Dec 28 2021 *)

Prog

(PARI) isok(k) = sumdiv(k, d, bigomega(d)==2) == 8; \\ Michel Marcus, Dec 28 2021

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), A350373 (k=6), A350374 (k=7), this sequence (k=8).

Sequence in context: A144563 A175746 A291714 * A179690 A350039 A158737

Adjacent sequences: A350372 A350373 A350374 * A350376 A350377 A350378

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 27 2021

Status

approved