A074471 Sum of 2nd, 4th, 6th, 8th and 10th powers of divisors are divisible by sum of divisors.

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

Links

Table of n, a(n) for n=1..32.

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

Adjacent sequences: A074468 A074469 A074470 * A074472 A074473 A074474

Keyword

nonn

Author

Labos Elemer, Sep 17 2002

Status

approved