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A334454
Number of distinct composite numbers in the n X n multiplication table.
2
0, 1, 3, 6, 10, 14, 20, 25, 31, 37, 47, 53, 65, 73, 82, 90, 106, 115, 133, 143, 155, 167, 189, 199, 215, 229, 244, 257, 285, 297, 327, 342, 360, 378, 398, 411, 447, 467, 488, 504, 544, 561, 603, 623, 644, 668, 714, 731, 762, 784, 811, 834, 886
OFFSET
1,3
COMMENTS
Number of distinct products i*j for 2<=i<=j<=n. - Chai Wah Wu, Oct 14 2023
EXAMPLE
There are a(7) = 20 distinct composite numbers in the 7x7 multiplication table:
1 2 3 4 5 6 7
4* 6* 8* 10* 12 14*
9* 12* 15* 18* 21*
16* 20* 24* 28*
25* 30* 35*
36* 42*
49*
MAPLE
A334454 := proc(n)
local dcom, i, j;
dcom := {} ;
for i from 1 to n do
for j from 1 to i do
if not isprime(i*j) and i*j> 1 then
dcom := dcom union {i*j} ;
end if;
end do:
end do:
print(n, dcom) ;
nops(dcom) ;
end proc:
seq(A334454(n), n=1..70) ; # R. J. Mathar, Oct 02 2020
PROG
(Python)
def A334454(n): return len({i*j for i in range(2, n+1) for j in range(2, i+1)}) # Chai Wah Wu, Oct 14 2023
CROSSREFS
Sequence in context: A024928 A330257 A079552 * A236758 A272058 A244360
KEYWORD
nonn
AUTHOR
Charles Kusniec, Sep 08 2020
STATUS
approved