%I #24 Jan 25 2024 07:16:11
%S 72474,106674,193026,237522,261478,308649,342066,370785,391674,491322,
%T 604878,865974,885477,931022,938598,1005630,1070727,1152822,1186926,
%U 1206822,1289978,1306878,1363326,1371774,1392726,1412918,1455249,1528111,1634227,1654678,1688478
%N Tetraprime numbers differing by more than 3 from any other squarefree number.
%C Tetraprimes are the product of four distinct prime numbers (cf. A046386).
%e 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.
%t 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 *)
%Y Cf. A046386, A013929. Subsequence of A268332.
%K nonn
%O 1,1
%A _Massimo Kofler_, Jan 19 2024
