cp's OEIS Frontend

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

%I A334454 #22 Oct 14 2023 10:54:27
%S A334454 0,1,3,6,10,14,20,25,31,37,47,53,65,73,82,90,106,115,133,143,155,167,
%T A334454 189,199,215,229,244,257,285,297,327,342,360,378,398,411,447,467,488,
%U A334454 504,544,561,603,623,644,668,714,731,762,784,811,834,886
%N A334454 Number of distinct composite numbers in the n X n multiplication table.
%C A334454 Number of distinct products i*j for 2<=i<=j<=n. - _Chai Wah Wu_, Oct 14 2023
%e A334454 There are a(7) = 20 distinct composite numbers in the 7x7 multiplication table:
%e A334454 1   2   3   4   5   6   7
%e A334454     4*  6*  8* 10* 12  14*
%e A334454         9* 12* 15* 18* 21*
%e A334454            16* 20* 24* 28*
%e A334454                25* 30* 35*
%e A334454                    36* 42*
%e A334454                        49*
%p A334454 A334454 := proc(n)
%p A334454     local dcom,i,j;
%p A334454     dcom := {} ;
%p A334454     for i from 1 to n do
%p A334454         for j from 1 to i do
%p A334454             if not isprime(i*j) and i*j> 1 then
%p A334454                 dcom := dcom union {i*j} ;
%p A334454             end if;
%p A334454         end do:
%p A334454     end do:
%p A334454     print(n,dcom) ;
%p A334454     nops(dcom) ;
%p A334454 end proc:
%p A334454 seq(A334454(n),n=1..70) ; # _R. J. Mathar_, Oct 02 2020
%o A334454 (Python)
%o A334454 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
%Y A334454 Cf. A027424, A333996.
%K A334454 nonn
%O A334454 1,3
%A A334454 _Charles Kusniec_, Sep 08 2020