A378097 -id:A378097 - cp's OEIS frontend

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

Massimo Kofler, Dec 02 2024

nonn

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

			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.

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

Intersection of A067885 and A124936.

Cf. A001358, A378097.

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

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 *)

Edited by Robert Israel, Feb 03 2025

A379167 Table read by row, where T(n,k), n>0 and k>0, represents the smallest n-digit number that is the product of k distinct primes and is sandwiched between semiprime numbers, or -1 if no such number exists.

Original entry on oeis.org

5, -1, 34, -1, 122, 186, 870, -1, 1042, 1146, 1190, 5610, -1, 10118, 10002, 10030, 10230, 39270, -1, 100462, 100158, 100030, 100122, 110670, 881790, -1, 1000478, 1000022, 1000010, 1000758, 1001130, 1009470, -1, 10000202, 10000258, 10000002, 10000218, 10001670, 10010910, 15825810

Offset: 1

Jean-Marc Rebert, Dec 17 2024

			Smallest n-digit numbers m product of k distinct primes sandwiched between two semiprimes m-1 and m+1:
  n k    m-1,           m,               m+1
  1 1   4 = 2^2,      5 = 5,            6 = 2 * 3;
  2 2  33 = 3 * 11,  34 = 2 * 17,      35 = 5 * 7;
  3 3 185 = 5 * 37, 186 = 2 * 3 * 31, 187 = 11 * 17;
Table read by rows:
   5;
  -1,       34;
  -1,      122,      186,      870;
  -1,     1042,     1146,     1190,     5610;
  -1,    10118,    10002,    10030,    10230,    39270;
  -1,   100462,   100158,   100030,   100122,   110670,   881790;
  -1,  1000478,  1000022,  1000010,  1000758,  1001130,  1009470;
  -1, 10000202, 10000258, 10000002, 10000218, 10001670, 10010910, 15825810;
  ...

Cf. A001358, A067885, A378627, A378097.

cp's OEIS Frontend

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

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