%I #14 Sep 20 2024 06:26:47

%S 18446,39766,74306,83434,94106,100346,107966,111154,111814,113366,

%T 140834,144754,145606,146014,147406,149854,154946,155702,156146,

%U 165346,171786,189034,190618,191806,197354,201686,203314,206194,211394,211946,219386,231286,234394,253114,258266,262294,263966

%N Sphenic numbers that are sandwiched between products of exactly 4 distinct primes (or tetraprimes).

%C Terms are of the form 4*k+2.

%e 18446 = 2 * 23 * 401 (between 18445 = 5*7*17*31 and 18447 = 3*11*13*43).

%e 39766 = 2 * 59 * 337 (between 39765 = 3*5*11*241 and 39767 = 7*13*19*23).

%e 74306 = 2 * 53 * 701 (between 74305 = 5*7*11*193 and 74307 = 3*17*31*47).

%p N:= 5*10^5: # for terms <= N

%p P:= select(isprime,[seq(i,i=3..N/3,2)]): nP:= nops(P):

%p R:= NULL:

%p for i from 1 to nP while 2*P[i]*P[i+1] <= N do

%p for j from i+1 to nP do

%p x:= 2*P[i]*P[j];

%p if x > N then break fi;

%p if numtheory:-bigomega(x-1) = 4 and numtheory:-bigomega(x+1) = 4 and

%p numtheory:-issqrfree(x-1) and numtheory:-issqrfree(x+1) then

%p R:= R,x

%p fi

%p od od:

%p sort([R]); # _Robert Israel_, Sep 02 2024

%t e[n_] := FactorInteger[n][[;; , 2]]; SequencePosition[e /@ Range[300000], {{1, 1, 1, 1}, {1, 1, 1}, {1, 1, 1, 1}}][[;; , 1]] + 1 (* _Amiram Eldar_, Sep 02 2024 *)

%Y Cf. A007304, A046386. Subsequence of A075819.

%K nonn

%O 1,1

%A _Massimo Kofler_, Sep 02 2024