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A046764
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Sum of the 4th powers of the divisors of n is divisible by n.
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5
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1, 34, 84, 156, 364, 492, 1092, 3444, 5617, 6396, 11234, 22468, 33628, 44772, 67404, 100884, 157276, 190978, 292084, 435708, 437164, 471828, 549687, 569772, 709937, 742612, 763912, 876252, 986076, 1099374, 1118480, 1289484, 1311492, 1419874
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OFFSET
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1,2
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COMMENTS
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Compare with multiply perfect numbers, A007691. Here Sum[ divisors ] is replaced by Sum[ 4th powers of divisors ].
Problem 11090 proves that this sequence is infinite. - T. D. Noe, Apr 18 2006
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LINKS
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FORMULA
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Mod[ Sigma [ 4, n ], n ]=0.
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EXAMPLE
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n=84, Sigma[ 4,84 ] = Sum(d^4) = 53771172 = 640133*84 = 640133*n;
n=5617, Sigma[ 4,5617 ] = 995446331475844 = 5617*17722083332, a multiple of n.
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MATHEMATICA
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Do[If[Mod[DivisorSigma[4, n], n]==0, Print[n]], {n, 1, 2*10^6}]
Select[Range[1500000], Divisible[DivisorSigma[4, #], #]&] (* Harvey P. Dale, Jun 25 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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