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A245644 Numbers n such that n^3 is an arithmetic number.

%I A245644 #29 Dec 01 2014 00:23:43
%S A245644 1,3,5,7,11,13,14,15,17,19,21,23,24,29,31,33,35,37,39,41,42,43,46,47,
%T A245644 51,52,53,55,56,57,59,61,62,65,66,67,69,70,71,73,77,79,80,83,85,87,89,
%U A245644 91,93,94,95,97,101,103,105,107,109,111,113,114,115,117,119,120,123,127,129,131,133,137,138,139
%N A245644 Numbers n such that n^3 is an arithmetic number.
%C A245644 A065091 is a subsequence.
%H A245644 Reinhard Zumkeller and Jens Kruse Andersen, <a href="/A245644/b245644.txt">Table of n, a(n) for n = 1..10000</a> (first 147 terms from Reinhard Zumkeller)
%H A245644 Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>
%F A245644 A245656(a(n)^3) = 1. - _Reinhard Zumkeller_, Jul 28 2014
%p A245644 isArithPow := proc(n,e)
%p A245644     local dvs,d ;
%p A245644     dvs := numtheory[divisors](n^e) ;
%p A245644     add(d,d=dvs)/nops(dvs) ;
%p A245644     if type(%,'integer') then
%p A245644         true;
%p A245644     else
%p A245644         false;
%p A245644     end if;
%p A245644 end proc:
%p A245644 for n to 300 do
%p A245644     if isArithPow(n,3) then
%p A245644         printf("%d,",n) ;
%p A245644     end if;
%p A245644 end do:
%t A245644 Select[Range[120], IntegerQ[DivisorSigma[1, #^3 ]/DivisorSigma[0, #^3 ]] &] (* _Michael De Vlieger_, Aug 05 2014 after _Stefan Steinerberger_ at A003601 *)
%o A245644 (Haskell)
%o A245644 a245644 n = a245644_list !! (n-1)
%o A245644 a245644_list = filter ((== 1) . a245656 . (^ 3)) [1..]
%o A245644 -- _Reinhard Zumkeller_, Jul 28 2014
%o A245644 (Python) from sympy import divisors, divisor_count
%o A245644 [n for n in range(1,10**3) if not sum(divisors(n**3)) % divisor_count(n**3)] # _Chai Wah Wu_, Aug 04 2014
%Y A245644 Cf. A003601, A107924, A107925.
%Y A245644 Cf. A245656.
%K A245644 nonn
%O A245644 1,2
%A A245644 _R. J. Mathar_, Jul 28 2014