A391322 a(n) is the smallest number not yet in the sequence that shares at least 3 prime factors (repetitions allowed) with a(n-1); a(1)=8.

8, 16, 24, 12, 36, 18, 54, 27, 81, 108, 48, 32, 40, 20, 60, 30, 90, 45, 135, 162, 72, 56, 28, 84, 42, 126, 63, 189, 216, 64, 80, 88, 44, 132, 66, 198, 99, 297, 243, 270, 120, 96, 104, 52, 156, 78, 234, 117, 351, 324, 144, 112, 128, 136, 68, 204, 102, 306

Offset

1,1

Links

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

Example

a(19)=135 shares the primes 3,3,5 with a(18)=45.
a(20)=162 shares the primes 3,3,3 with a(19)=135.
a(21)=72 shares the primes 2,3,3 with a(20)=162.

Maple

N:= 1000: # for terms before the first term > N
Cands:= [$1..7, $9..N]: nC:= N-1:
R:= 8: x:= 8: found:= true:
while found do
  found:= false;
  for i from 1 to nC do
    if numtheory:-bigomega(igcd(x, Cands[i])) >= 3 then
      x:= Cands[i];
      R:= R, x;
      Cands:= subsop(i=NULL, Cands);
      nC:= nC-1;
      found:= true;
      break
  fi od;
od:
R; # Robert Israel, Dec 07 2025

Crossrefs

Cf. A251756 (2 prime factors).

Sequence in context: A254141 A188438 A282256 * A037370 A325261 A389599

Adjacent sequences: A391319 A391320 A391321 * A391323 A391324 A391325

Keyword

nonn

Author

Enrique Navarrete, Dec 06 2025

Status

approved