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

18446, 39766, 74306, 83434, 94106, 100346, 107966, 111154, 111814, 113366, 140834, 144754, 145606, 146014, 147406, 149854, 154946, 155702, 156146, 165346, 171786, 189034, 190618, 191806, 197354, 201686, 203314, 206194, 211394, 211946, 219386, 231286, 234394, 253114, 258266, 262294, 263966

Offset: 1

Author

Massimo Kofler, Sep 02 2024

Keywords

• nonn

Comments

Terms are of the form 4*k+2.

Examples

			18446 = 2 * 23 * 401  (between 18445 = 5*7*17*31 and 18447 = 3*11*13*43).
39766 = 2 * 59 * 337  (between 39765 = 3*5*11*241 and 39767 = 7*13*19*23).
74306 = 2 * 53 * 701  (between 74305 = 5*7*11*193 and 74307 = 3*17*31*47).
		

Crossrefs

Cf. A007304, A046386. Subsequence of A075819.

Programs

Maple

N:= 5*10^5: # for terms <= N
P:= select(isprime,[seq(i,i=3..N/3,2)]): nP:= nops(P):
R:= NULL:
for i from 1 to nP while 2*P[i]*P[i+1] <= N do
  for j from i+1 to nP do
    x:= 2*P[i]*P[j];
    if x > N then break fi;
    if numtheory:-bigomega(x-1) = 4 and numtheory:-bigomega(x+1) = 4 and
      numtheory:-issqrfree(x-1) and numtheory:-issqrfree(x+1) then
        R:= R,x
    fi
od od:
sort([R]); # Robert Israel, Sep 02 2024

Mathematica

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 *)