A334454 Number of distinct composite numbers in the n X n multiplication table.

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

Links

Table of n, a(n) for n=1..53.

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

Cf. A027424, A333996.

Sequence in context: A024928 A330257 A079552 * A236758 A272058 A244360

Adjacent sequences: A334451 A334452 A334453 * A334455 A334456 A334457

Keyword

nonn

Author

Charles Kusniec, Sep 08 2020

Status

approved