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%I #28 Feb 17 2024 10:32:34
%S 1,34,84,156,364,492,1092,3444,5617,6396,11234,22468,33628,44772,
%T 67404,100884,157276,190978,292084,435708,437164,471828,549687,569772,
%U 709937,742612,763912,876252,986076,1099374,1118480,1289484,1311492,1419874
%N Sum of the 4th powers of the divisors of n is divisible by n.
%C Compare with multiply perfect numbers, A007691. Here Sum[ divisors ] is replaced by Sum[ 4th powers of divisors ].
%C Problem 11090 proves that this sequence is infinite. - _T. D. Noe_, Apr 18 2006
%H Amiram Eldar, <a href="/A046764/b046764.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..200 from T. D. Noe)
%H Florian Luca and John Ferdinands, <a href="https://www.jstor.org/stable/27641939">Problem 11090: Sometimes n divides sigma_k(n)</a>, Amer. Math. Monthly 113:4 (2006), pp. 372-373.
%F Mod[ Sigma [ 4, n ], n ]=0.
%e n=84, Sigma[ 4,84 ] = Sum(d^4) = 53771172 = 640133*84 = 640133*n;
%e n=5617, Sigma[ 4,5617 ] = 995446331475844 = 5617*17722083332, a multiple of n.
%t Do[If[Mod[DivisorSigma[4, n], n]==0, Print[n]], {n, 1, 2*10^6}]
%t Select[Range[1500000],Divisible[DivisorSigma[4,#],#]&] (* _Harvey P. Dale_, Jun 25 2014 *)
%o (PARI) is(n)=sigma(n, 4)%n==0 \\ _Charles R Greathouse IV_, Feb 04 2013
%Y Cf. A001159, A007691.
%K nonn
%O 1,2
%A _Labos Elemer_
%E More terms from _Robert G. Wilson v_, Jun 09 2000
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