The number N is a sum of 4 different numbers, each being a square of one of the 4 smallest divisors of N (e.g. N=36 does not qualify since 1^2+2^2+3^2+4^2
sums up to 30, not 36.)

Provide a full list of similar numbers or show that none exist.

Two software notes:

Here is the Gnu Fortran version of the same routine for comparison.

Also, I worry about Charlie's cutoff of "sr=sqr(N)"

This would have missed, e.g., 3 as a factor of 6 (I think).

(I note this because I did the same thing at first.)

(Later... thinking it over, this makes sense since we can't use factors greater than sqrt(N) for the sum. Never mind!)

         program dd

        implicit none

        integer list(4),i,j,k,jj,cnt

           do 1 i=1,100000

           cnt=0

                do k=1,i

                    if(k*int((1.*i)/k).eq.i)then

                    cnt=cnt+1

                    list(cnt)=k

                        if(cnt.eq.4)then

        jj=list(1)**2+list(2)**2+list(3)**2+list(4)**2

                            if(jj.eq.i)then

                            print*,' solved: ',i,list

                            go to 1

                            else

                            go to 1

                            endif

                        endif

                    endif

                enddo

1           enddo

        end

rabbit-3:~ lord$ dd

  solved:   130  1  2  5  10

Edited on July 9, 2018, 2:49 am

Edited on July 9, 2018, 6:21 pm

Posted by Steven Lord on 2018-07-08 22:59:26