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A375908
Sphenic numbers that are sandwiched between products of exactly 4 distinct primes (or tetraprimes).
0
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
1,1
COMMENTS
Terms are of the form 4*k+2.
EXAMPLE
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).
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 *)
CROSSREFS
Cf. A007304, A046386. Subsequence of A075819.
Sequence in context: A231142 A251874 A035924 * A209895 A190110 A157738
KEYWORD
nonn
AUTHOR
Massimo Kofler, Sep 02 2024
STATUS
approved