A369238 Tetraprime numbers differing by more than 3 from any other squarefree number.

72474, 106674, 193026, 237522, 261478, 308649, 342066, 370785, 391674, 491322, 604878, 865974, 885477, 931022, 938598, 1005630, 1070727, 1152822, 1186926, 1206822, 1289978, 1306878, 1363326, 1371774, 1392726, 1412918, 1455249, 1528111, 1634227, 1654678, 1688478

Offset

1,1

Comments

Tetraprimes are the product of four distinct prime numbers (cf. A046386).

Links

Robert Israel, Table of n, a(n) for n = 1..5415

Example

72474 = 2 * 3 * 47 * 257 is a tetraprime; 72471 = 3 * 7^2 * 17 * 29, 72472 = 2^3 * 9059, 72473 = 23^2 * 137, 72475 = 5^2 * 13 * 223, 72476 = 2^2 * 18119, 72477 = 3^2 * 8053 are all nonsquarefree numbers, so 72474 is a term.

Maple

N:= 3*10^6: # for terms <= N
P:= select(isprime, [2, seq(i, i=3 .. N/30, 2)]): nP:= nops(P):
filter:= proc(x) not ormap(numtheory:-issqrfree, [x-3, x-2, x-1, x+1, x+2, x+3]) end proc:
R:= NULL:
for i1 from 1 to nP do
  r1:= P[i1];
  for i2 from 1 to i1-1 do
    r2:= r1 * P[i2]; if r2 > N/6 then break fi;
    for i3 from 1 to i2-1 do
      r3:= r2 * P[i3]; if r3 > N/2 then break fi;
      for i4 from 1 to i3-1 do
        r:= r3 * P[i4];
        if r > N then break fi;
        if filter(r) then R:= R, r; fi
od od od od:
sort([R]); # Robert Israel, Jan 19 2025

Mathematica

f[n_] := Module[{e = FactorInteger[n][[;; , 2]], p}, p = Times @@ e; If[p > 1, 0, If[e == {1, 1, 1, 1}, 1, -1]]]; SequencePosition[Array[f, 2*10^6], {0, 0, 0, 1, 0, 0, 0}][[;; , 1]] + 3 (* Amiram Eldar, Jan 19 2024 *)

Crossrefs

Cf. A046386, A013929. Subsequence of A268332.

Sequence in context: A126658 A251340 A183788 * A093212 A114258 A238151

Adjacent sequences: A369235 A369236 A369237 * A369239 A369240 A369241

Keyword

nonn

Author

Massimo Kofler, Jan 19 2024

Status

approved