A378627 Products of 6 distinct primes that are sandwiched between semiprime numbers.

39270, 66990, 71610, 79170, 82110, 99330, 110670, 122430, 123690, 125970, 129030, 132090, 136290, 144690, 152490, 163590, 166530, 167790, 180642, 182910, 190190, 191730, 215670, 220110, 222222, 226590, 227766, 231990, 235410, 239190, 247170, 248710, 249690, 254562, 258258, 260130

Offset

1,1

Comments

All terms are even.

Not all terms are divisible by 6: the first that is not is a(21) = 190190. The first term that is deficient is a(1966) = 4739702. - Robert Israel, Feb 03 2025

Links

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

Example

39270 is a term because 39270=2*3*5*7*11*17 is the product of six distinct primes, 39269=107*367 and 39271=173*227 are both semiprimes.
66990 is a term because 66990=2*3*5*7*11*29 is the product of six distinct primes, 66989=13*5153 and 66991=31*2161 are both semiprimes.

Maple

with(priqueue):
children:= proc(t) local R, i, pp;
   R:= NULL:
   pp:= nextprime(t[6]);
   for i from 6 to 2 by -1 do
     R:= R, [t[1]*pp/t[i], op(t[2..i-1]), op(t[i+1..6]), pp];
     if t[i-1] <> prevprime(t[i]) then break fi;
   od;
   {R}
end proc:
Res:= NULL: count:= 0:
initialize(pq):
insert([-2*mul(ithprime(i), i=2..6), 3, 5, 7, 11, 13], pq);
while count < 100 do
  t:= extract(pq);
  if numtheory:-bigomega(-t[1]-1) = 2 and numtheory:-bigomega(-t[1]+1) = 2 then
    Res:= Res, -t[1]; count:= count+1;
  fi;
  for tt in children(t) do insert(tt, pq) od:
od:
Res; # Robert Israel, Feb 03 2025

Mathematica

SequencePosition[Array[FactorInteger[#][[;; , 2]] &, 270000] /. {2} -> {1, 1}, {{1, 1}, {1, 1, 1, 1, 1, 1}, {1, 1}}][[;; , 1]] + 1 (* Amiram Eldar, Dec 02 2024 *)

Crossrefs

Intersection of A067885 and A124936.

Cf. A001358, A378097.

Sequence in context: A250515 A031667 A196200 * A274128 A144306 A234033

Adjacent sequences: A378624 A378625 A378626 * A378628 A378629 A378630

Keyword

nonn

Author

Massimo Kofler, Dec 02 2024

Extensions

Edited by Robert Israel, Feb 03 2025

Status

approved