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%I #5 Oct 15 2013 22:31:30
%S 1,64,729,1024,2916,4096,14580,15625,46656,59049,62500,65536,117649,
%T 142884,186624,242757,262144,348480,364500,478953,531441,714420,
%U 746496,796797,933120,1000000,1032256,1771561,2985984,3062500,3172608,3187188
%N Sum of 2nd, 4th, 6th, 8th and 10th powers of divisors are divisible by sum of divisors.
%e m=64,s1=127,{s2/127,s4/127,s6/127,s8/127,s10/127}= {1,43,140911,549687103,2225029922431,9086996103150463}; m=14580=54.54.5. Known cases show that terms are either squares or p.square, where p is a prime of 4k+1 form.
%t Select[Range[3200000],And@@Divisible[DivisorSigma[2Range[5],#], DivisorSigma[ 1,#]]&] (* _Harvey P. Dale_, Apr 10 2013 *)
%K nonn
%O 1,2
%A _Labos Elemer_, Sep 17 2002