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

Author

Massimo Kofler, Jan 19 2024

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A046386, A013929. Subsequence of A268332.

Programs

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 *)