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A350374
Numbers with exactly 7 semiprime divisors.
6
420, 630, 660, 780, 840, 924, 990, 1020, 1050, 1092, 1140, 1170, 1320, 1380, 1386, 1428, 1470, 1530, 1540, 1560, 1596, 1638, 1650, 1680, 1710, 1716, 1740, 1820, 1848, 1860, 1890, 1932, 1950, 2040, 2070, 2142, 2184, 2220, 2244, 2280, 2380, 2394, 2436, 2460, 2508, 2550
OFFSET
1,1
COMMENTS
Numbers with prime signature {1,1,1,k} with k >= 2. - Robert Israel, Nov 09 2025
LINKS
MAPLE
N:= 10^4: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N/(2^2*3*5), 2)]):
nP:= nops(P):
Res:= NULL:
for i1 from 1 to nP do
p1:= P[i1];
for i2 from i1+1 to nP do
p2:= P[i2];
if p1 * p2 * 3 * 4 > N then break fi;
for i3 from i2 + 1 to nP do
p3:= P[i3];
if p1 * p2 * p3 * 4 > N then break fi;
for i4 from 1 to nP do
if member(i4, {i1, i2, i3}) then next fi;
p4:= P[i4];
for n4 from 2 do
x:= p1 * p2 * p3 * p4^n4;
if x > N then break fi;
Res:= Res, x
od od od od od:
Res:= sort([Res]); # Robert Israel, Nov 09 2025
MATHEMATICA
q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 7; Select[Range[2500], q] (* Amiram Eldar, Dec 28 2021 *)
PROG
(PARI) isok(k) = sumdiv(k, d, bigomega(d)==2) == 7; \\ Michel Marcus, Dec 28 2021
CROSSREFS
Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), A350373 (k=6), this sequence (k=7), A350375 (k=8).
Sequence in context: A024410 A200521 A380432 * A189982 A376374 A070237
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Dec 27 2021
STATUS
approved