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A020486 Average of squares of divisors is an integer: numbers k such that sigma_0(k) divides sigma_2(k).

%I A020486 #33 Jun 15 2024 05:48:22
%S A020486 1,3,4,5,7,11,12,13,15,17,19,20,21,23,25,27,28,29,31,33,35,37,39,41,
%T A020486 43,44,47,48,49,51,52,53,55,57,59,60,61,65,67,68,69,71,73,75,76,77,79,
%U A020486 83,84,85,87,89,91,92,93,95,97,100,101,103,105,107,108,109,111,112,113,115,116
%N A020486 Average of squares of divisors is an integer: numbers k such that sigma_0(k) divides sigma_2(k).
%C A020486 If sigma_2(k)/sigma_0(k) is a square then k is an RMS-number (A140480). - _Ctibor O. Zizka_, Jul 14 2008
%H A020486 Amiram Eldar, <a href="/A020486/b020486.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%F A020486 A001157(k) mod A000005(k) = 0. - _Reinhard Zumkeller_, Jan 15 2013
%t A020486 Select[Range[150],Divisible[DivisorSigma[2,#],DivisorSigma[0,#]]&] (* _Harvey P. Dale_, May 03 2011 *)
%o A020486 (Haskell)
%o A020486 a020486 n = a020486_list !! (n-1)
%o A020486 a020486_list = filter (\x -> a001157 x `mod` a000005 x == 0) [1..]
%o A020486 -- _Reinhard Zumkeller_, Jan 15 2013
%o A020486 (Magma) [n: n in [1..120] | IsZero(DivisorSigma(2, n) mod NumberOfDivisors(n))]; // _Bruno Berselli_, Apr 11 2013
%o A020486 (PARI) is(n)=sigma(n,2)%numdiv(n)==0 \\ _Charles R Greathouse IV_, Jul 02 2013
%Y A020486 Cf. A000005, A001157, A140480.
%K A020486 nonn
%O A020486 1,2
%A A020486 _David W. Wilson_