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A245644 Numbers n such that n^3 is an arithmetic number. 2

%I

%S 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 51,52,53,55,56,57,59,61,62,65,66,67,69,70,71,73,77,79,80,83,85,87,89,

%U 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 Numbers n such that n^3 is an arithmetic number.

%C A065091 is a subsequence.

%H 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 Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>

%F A245656(a(n)^3) = 1. - _Reinhard Zumkeller_, Jul 28 2014

%p isArithPow := proc(n,e)

%p local dvs,d ;

%p dvs := numtheory[divisors](n^e) ;

%p add(d,d=dvs)/nops(dvs) ;

%p if type(%,'integer') then

%p true;

%p else

%p false;

%p end if;

%p end proc:

%p for n to 300 do

%p if isArithPow(n,3) then

%p printf("%d,",n) ;

%p end if;

%p end do:

%t Select[Range[120], IntegerQ[DivisorSigma[1, #^3 ]/DivisorSigma[0, #^3 ]] &] (* _Michael De Vlieger_, Aug 05 2014 after _Stefan Steinerberger_ at A003601 *)

%o (Haskell)

%o a245644 n = a245644_list !! (n-1)

%o a245644_list = filter ((== 1) . a245656 . (^ 3)) [1..]

%o -- _Reinhard Zumkeller_, Jul 28 2014

%o (Python) from sympy import divisors, divisor_count

%o [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 Cf. A003601, A107924, A107925.

%Y Cf. A245656.

%K nonn

%O 1,2

%A _R. J. Mathar_, Jul 28 2014

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Last modified December 12 07:17 EST 2018. Contains 318053 sequences. (Running on oeis4.)