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A375908 Sphenic numbers that are sandwiched between products of exactly 4 distinct primes (or tetraprimes).

%I A375908 #14 Sep 20 2024 06:26:47
%S A375908 18446,39766,74306,83434,94106,100346,107966,111154,111814,113366,
%T A375908 140834,144754,145606,146014,147406,149854,154946,155702,156146,
%U A375908 165346,171786,189034,190618,191806,197354,201686,203314,206194,211394,211946,219386,231286,234394,253114,258266,262294,263966
%N A375908 Sphenic numbers that are sandwiched between products of exactly 4 distinct primes (or tetraprimes).
%C A375908 Terms are of the form 4*k+2.
%e A375908 18446 = 2 * 23 * 401  (between 18445 = 5*7*17*31 and 18447 = 3*11*13*43).
%e A375908 39766 = 2 * 59 * 337  (between 39765 = 3*5*11*241 and 39767 = 7*13*19*23).
%e A375908 74306 = 2 * 53 * 701  (between 74305 = 5*7*11*193 and 74307 = 3*17*31*47).
%p A375908 N:= 5*10^5: # for terms <= N
%p A375908 P:= select(isprime,[seq(i,i=3..N/3,2)]): nP:= nops(P):
%p A375908 R:= NULL:
%p A375908 for i from 1 to nP while 2*P[i]*P[i+1] <= N do
%p A375908   for j from i+1 to nP do
%p A375908     x:= 2*P[i]*P[j];
%p A375908     if x > N then break fi;
%p A375908     if numtheory:-bigomega(x-1) = 4 and numtheory:-bigomega(x+1) = 4 and
%p A375908       numtheory:-issqrfree(x-1) and numtheory:-issqrfree(x+1) then
%p A375908         R:= R,x
%p A375908     fi
%p A375908 od od:
%p A375908 sort([R]); # _Robert Israel_, Sep 02 2024
%t A375908 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 A375908 Cf. A007304, A046386. Subsequence of A075819.
%K A375908 nonn
%O A375908 1,1
%A A375908 _Massimo Kofler_, Sep 02 2024