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A074471
Sum of 2nd, 4th, 6th, 8th and 10th powers of divisors are divisible by sum of divisors.
0
1, 64, 729, 1024, 2916, 4096, 14580, 15625, 46656, 59049, 62500, 65536, 117649, 142884, 186624, 242757, 262144, 348480, 364500, 478953, 531441, 714420, 746496, 796797, 933120, 1000000, 1032256, 1771561, 2985984, 3062500, 3172608, 3187188
OFFSET
1,2
EXAMPLE
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.
MATHEMATICA
Select[Range[3200000], And@@Divisible[DivisorSigma[2Range[5], #], DivisorSigma[ 1, #]]&] (* Harvey P. Dale, Apr 10 2013 *)
CROSSREFS
Sequence in context: A274219 A161861 A179149 * A164345 A164337 A354178
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 17 2002
STATUS
approved