Find the smallest positive integer n such that n has exactly 144 distinct positive divisors and there are 10 consecutive integers among them (Note: 1 and n are both divisors of n)
(In reply to
computer solution by Charlie)
MATLAB enables a more elegant (computer-wise) solution:
clearvars, clc
for n=10:1000000
d=properDivisors(n);
if length(d)==143
good=false; consec=0;
for i=2:length(d)
if d(i)==d(i-1)+1
consec=consec+1;
if consec==9
good=true;
break
end
else
consec=0;
end
end
if good
disp(n)
disp(d(i-9:i))
end
end
end
function y=properDivisors(x)
y=1;z=[];
sr=sqrt(x);
for i=2:sr
if mod(x,i)==0
y=[y i];
if i~=sr
z=[x/i z];
end
end
end
y=[y z];
end
110880
1 2 3 4 5 6 7 8 9 10
131040
1 2 3 4 5 6 7 8 9 10
138600
1 2 3 4 5 6 7 8 9 10
151200
1 2 3 4 5 6 7 8 9 10
163800
1 2 3 4 5 6 7 8 9 10
171360
1 2 3 4 5 6 7 8 9 10
191520
1 2 3 4 5 6 7 8 9 10
194040
1 2 3 4 5 6 7 8 9 10
201600
1 2 3 4 5 6 7 8 9 10
211680
1 2 3 4 5 6 7 8 9 10
214200
1 2 3 4 5 6 7 8 9 10
229320
1 2 3 4 5 6 7 8 9 10
231840
1 2 3 4 5 6 7 8 9 10
239400
1 2 3 4 5 6 7 8 9 10
241920
1 2 3 4 5 6 7 8 9 10
252000
1 2 3 4 5 6 7 8 9 10
264600
1 2 3 4 5 6 7 8 9 10
272160
1 2 3 4 5 6 7 8 9 10
282240
1 2 3 4 5 6 7 8 9 10
289800
1 2 3 4 5 6 7 8 9 10
292320
1 2 3 4 5 6 7 8 9 10
299880
1 2 3 4 5 6 7 8 9 10
304920
1 2 3 4 5 6 7 8 9 10
312480
1 2 3 4 5 6 7 8 9 10
335160
1 2 3 4 5 6 7 8 9 10
340200
1 2 3 4 5 6 7 8 9 10
365400
1 2 3 4 5 6 7 8 9 10
372960
1 2 3 4 5 6 7 8 9 10
390600
1 2 3 4 5 6 7 8 9 10
405720
1 2 3 4 5 6 7 8 9 10
413280
1 2 3 4 5 6 7 8 9 10
425880
1 2 3 4 5 6 7 8 9 10
433440
1 2 3 4 5 6 7 8 9 10
441000
1 2 3 4 5 6 7 8 9 10
466200
1 2 3 4 5 6 7 8 9 10
473760
1 2 3 4 5 6 7 8 9 10
476280
1 2 3 4 5 6 7 8 9 10
493920
1 2 3 4 5 6 7 8 9 10
511560
1 2 3 4 5 6 7 8 9 10
516600
1 2 3 4 5 6 7 8 9 10
534240
1 2 3 4 5 6 7 8 9 10
541800
1 2 3 4 5 6 7 8 9 10
546840
1 2 3 4 5 6 7 8 9 10
592200
1 2 3 4 5 6 7 8 9 10
594720
1 2 3 4 5 6 7 8 9 10
614880
1 2 3 4 5 6 7 8 9 10
617400
1 2 3 4 5 6 7 8 9 10
645120
1 2 3 4 5 6 7 8 9 10
652680
1 2 3 4 5 6 7 8 9 10
667800
1 2 3 4 5 6 7 8 9 10
675360
1 2 3 4 5 6 7 8 9 10
715680
1 2 3 4 5 6 7 8 9 10
723240
1 2 3 4 5 6 7 8 9 10
728280
1 2 3 4 5 6 7 8 9 10
735840
1 2 3 4 5 6 7 8 9 10
743400
1 2 3 4 5 6 7 8 9 10
758520
1 2 3 4 5 6 7 8 9 10
768600
1 2 3 4 5 6 7 8 9 10
796320
1 2 3 4 5 6 7 8 9 10
829080
1 2 3 4 5 6 7 8 9 10
836640
1 2 3 4 5 6 7 8 9 10
844200
1 2 3 4 5 6 7 8 9 10
894600
1 2 3 4 5 6 7 8 9 10
897120
1 2 3 4 5 6 7 8 9 10
909720
1 2 3 4 5 6 7 8 9 10
919800
1 2 3 4 5 6 7 8 9 10
934920
1 2 3 4 5 6 7 8 9 10
977760
1 2 3 4 5 6 7 8 9 10
995400
1 2 3 4 5 6 7 8 9 10
>>
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Posted by Charlie
on 2021-12-04 08:22:28 |
re: computer solution revisited
